MECH E4320 (Fall 2024): Homework #6 1. Resolve the 1-D chambered non-premixed flame problem solved in class but now for a system with PDF ≠ PDo ≠ λ/cp (but still with constant PDF , PDo , and λ/cp throughout the chamber) using only the reaction sheet assumption (since you cannot apply the simple coupling function presented in class to non-equidiffusive systems). Use th~e ~fact that~there are no reactions from 0 ≤ x
EXMBM514-24C (HAM) Economics and the Global Context What this paper is about This paper provides an introduction to the tools used to analyse and understand the economic environment in which individuals and businesses operate, and the role of government in shaping that environment. It will provide an introduction to the key characteristics of different types of economic environments from both a business and a policy perspective, the ways in which markets can be analysed, and an introduction to macroeconomic issues that are helpful for business decision-making. How this paper will be taught This is a FLEXI paper that will have learning available both face-to-face (on campus) and online, thereby offering flexibility in terms of where and how students learn. Students should confirm the timing and location of face-to-face and live (synchronous) sessions in Moodle. What you will study Topic Introduction to economics Demand, supply, and government policies Elasticity and its applications Consumers, producers, and the efficiency of markets Externalities Economics of decision-making: An introduction to game theory International trade Measuring a nation’s income, production, and growth Measuring the cost of living Saving, investment, and the financial system Unemployment Open-economy macroeconomics
FINN3021 Security Investment Analysis Undergraduate Programmes 2024/25 Summative Assignment During Epiphany Term you are required to construct an investment portfolio and manage and monitor its performance. The investment/portfolio construction period runs from Monday 27th January until Friday 21st March 2025. An initial fund of $1,000,000 is available to purchase assets (equities, bonds, mutual funds, and ETFs). The total number of transactions permitted for the assignment is limited to 300 for the investment period. You may use whatever platform. you wish to construct your portfolio e.g., StockTrak, Bloomberg etc., however, you must adhere to the parameters outlined above. Details of how to register for an individual StockTrak account (should you wish to use this platform) are outlined on the module’s Blackboard Learn Ultra site. Please note, however, that you should not reuse the same account that was used for the group formative assignment. The assignment will be assessed by means of an individual written report that critically addresses all of the following: • the investment philosophy that underpins the construction of the portfolio. • the investment strategy adopted in constructing your portfolio (your investment philosophy and strategy should be carefully distinguished from one another). • the nature of the prevailing economic and financial environment that shapes your investment decision-making and the potential impact of these on the performance of the portfolio. • the rationale for the allocation of assets between broad sectors and the principles that have guided the choice of individual securities (the application of technical and/or fundamental analysis). • the performance of the portfolio in relation to a chosen benchmark (and a justification for the choice of benchmark). • the risk/return characteristics of the portfolio using appropriate portfolio performance measures (consideration should be given to the performance of your portfolio in terms of security selection, market timing, and diversification). • the strengths and weaknesses of your investment strategy and how any lessons learned might alter your investment decision-making if you were asked to construct a new portfolio at the end of the simulation period. • Furthermore, the discussion above should be underpinned by appropriate academic and practitioner literature as necessary. • Finally, as this is an investment report, presentation is important, and elements expected in an investment report should be present e.g., such as charts, graphs, tables, section headings. Please note that the assignment will be assessed based on your written report and not on the performance of your portfolio over the investment period. Overall word limit: 3500 words
The following topics are covered in Quantitative Analysis II and are necessary background for Quant III courses.Since the Proficiency Exam is an open book exam, students may bring any econometrics statistics textbook with which they are comfortable. Multiple Regression I: Dummy Variables and Interactions (this is just carry-over from Quant) · Categorical Independent Variables o Understand the concept of the base (omitted) category o Be able to interpret b-coefficients for a set of (J - 1) dummy variables · Interaction terms o Understand and be able to interpret an interaction term that is the product of one or more dummies and a single continuous regressor o Understand and be able to interpret interaction terms that is a product of two dummy regressors Specification I: Choosing the Right Variables · Multiple Regression o Understand and be able to interpret standardized betas o Understand and be able to calculate and interpret the Adjusted R-square · Omitting a Relevant Independent Variable o Understand the consequences of omitting a relevant independent variable o Be able to anticipate the direction of omitted variable bias in an application · Including an Irrelevant Independent Variable o Understand the consequences of including an irrelevant independent variable Specification II: Correct Functional Form · Linear Functional Form. o Understand and be able to diagnose violations of linearity from scatterplot output · Linear-Log Models o Understand when you might want to use this model o Be able to interpret the slope coefficients (using the approximation) o Be able to interpret the b-coefficient for a logged X predictor by calculating consecutive predicted values and assessing the predicted change in Y that results from a change in X · Log-Linear Models o Understand when you might want to use this model o Be able to interpret the slope coefficients (using the approximation) · Log-Log Models o Understand when you might want to use this model o Be able to interpret the slope coefficient as an elasticity o Be able to calculate the expected value of the slope of curve any specific value of Xi′ · Polynomial Model (Quadratic) o Understand when you might want to use this model (based on theory and scatterplot) o Understand and be able to solve for and interpret the value of Xi′ at the turning point o Be able to calculate and interpret the slope of the curve at any value of Xi′ o Be able to calculate and interpret “marginal effects” of X on Y (i.e., the predicted change in Y for a one-unit change in X--at different levels of X—using predicted values) Multicollinearity · Meaning of Multicollinearity o Understand multicollinearity as a sample phenomenon o Understand the practical consequences of multicollinearity · Detecting Multicollinearity o Informally (compare individual t-values to measures of overall model fit, simple bivariate correlation coefficients) o Understand and be able to calculate and interpret Variance Inflation Factor · Correction Strategy for Multicollinearity o Understand and be able to evaluate and interpret possible correction strategies when given relevant information (i.e., word problem/description, STATA output) Heteroskedasticity · Meaning of Heteroskedasticity o Understand the meaning of (pure) heteroskedasticity o Understand the practical consequences of heteroskedasticity · Detecting Heteroskedasticity o Informally (plot of residuals against Xi’s, plot of residuals against predicted values) o Understand the motivations of the Breusch-Pagan and White tests § Understand the form. of heteroskedasticity being tested in each test o Be able to execute these tests and interpret their results § Understand and be able to apply the appropriate decision rule · Robust Standard Errors o Understand the motivation and calculation of robust standard errors o Understand and be able to interpret regression results that use robust standard errors Serial Correlation · Understand the problem of first-order serial correlation · Understand the practical consequences of first-order serial correlation · Detection of first-order serial correlation o Be able to perform. the Durbin-Watson d test · Robust Standard Errors o Understand the motivation behind robust standard errors o Understand and be able to interpret regression results that use Newey-West robust standard errors Linear Probability Model and Logit · Linear Probability Model o Understand the motivation and meaning of a binary dependent variable model o Understand the inherent problems with the LPM o Be able to interpret slope coefficients in a LPM · Binary Logistic Regression o Be able to calculate and interpret logit coefficients as odds ratios o Be able to calculate and interpret predicted probabilities (using the formula) and predicted probability changes (using relevant STATA output from margins/marginsplot) o Understand and be able to calculate and interpret the percentage of cases correctly predicted (using lstat) Difference in Differences · Understand the basic DID setup as a comparison of four sample means (i.e., Y’s) · Understand a DID setup with two independently pooled cross-sections · Understand a DID setup with two period of panel data on the same cross-sectional units · Be able to calculate and interpret the DID estimate in either of the two above setups · Understand the key identifying DID assumption (“common trends”), and how one might demonstrate emirically the plausibility of this assumption Instrumental Variables · Understand the idea of the four compliance types using a potential outcomes framework · Understand the econometric formulation of the IV estimand (two composite assumptions) · Understand and be able to compute the IV estimand as the ratio of two causal effects (i.e., the Wald estimate) o Understand the numerator (ITT) o Understand the denominator (causal effect of Z on D) · Be able to interpret 2SLS regression estimates (with and without covariates) · Understand how 2SLS can be extended to incorporate multiple instruments · Understand how 2SLS can be extended to incorporate a continuous treatment (D) Panel Data Methods · Understand how pooled OLS can be used when analyzing panel data (and what its limits are) · Understand how panel data can help with the problem of omitted variable bias · Understand how we control for unit fixed effects and time fixed effects · Understand how to assess between and within variation on the treatment variable · Understand how first-differencing eliminates the unit fixed effects prior to estimation o Understand how to interpret the coefficient estimates in first-differences models · Understand how to apply and interpret the deviations from the means estimator o Understand how to interpret the coefficient estimates o Understand xtreg, fe output (including post-estimation) · Understand how to apply and interpret the LSDV estimator o Understand how to interpret the coefficient estimates (included the estimated fixed effects) · Understand the key identifying assumptions behind fixed effects regression models
Assignment: Microsoft Word (10%) Word Long Document and Thesis Formatting This task is to test and allow you to show your competency in applying all the skill regarding long report and thesis formatting using MS Word Tools & Mendeley SW. This skill is important when you want to write and format your thesis at degree, master or PhD level. 1) Find a journal article with Min 8 pages: (5 Mark) a) Have min 3 tables b) Have min 3 figures c) Then do the following formatting and task 2) Basic formatting: (5 Mark) a) Alignment justify b) Font Times news roman 12 c) Line spacing 1.5 3) Make a Cover Page: (5 Mark) a) Put your picture. b) Your name and matric number. c) Article title. d) Other related content for front page. 4) Make a Table of Contents. (One page) (5 Mark) a) Main Headings (min 5 main heading) b) Sub-headings (2@3 subheading for level 2 & level 3 for each heading) c) After finish everything, Updating Table of Contents to show the latest update. 5) List of Tables. (5 Mark) a) Formatting all the tables (font size 11, single spacing, Title above the table, used table design tools) b) After finish everything, Updating List of Tables. 6) List of Figures (5 Mark) a) Resize the figures (chart, picture, model, diagram etc. Title below the figure) b) After finish everything, Updating List of Figures 7) Different Header (according to main heading title on page and Footer with your name & matric number and page number). (5 Mark) 8) Citation and Reference (show 5 references using Chicago Style) (5 Mark)
EXMBM512-24C (HAM) Leadership and Change Management What this paper is about Whāia te iti kahurangi ki te tūohu koe me he maunga teitei Seek the treasure you value most dearly: if you bow your head, let it be to a lofty mountain This whakatauki is about aiming high or for what is truly valuable, but its real message is to be persistent and to not let obstacles stop you from reaching your goal - My wish for you this trimester. Tēnā koutou. I am delighted to be with you during this learning journey – and during these internationally complex and changing times. We are in unknown and uncharted territory. However, this is an unprecedented opportunity to watch leadership history in the making. CLASS PHILOSOPHY AND TEACHING This course is intended to be experiential in nature. You will be invited to actively participate in or lead discussions of the various topics we will cover this trimester. Class activities will include collaborative reading and annotation of pertinent readings, in-class presentations by students as well as invited expert practitioners or scholars, and participating in class discussions. This classroom will provide a safe environment for you to rehearse your leadership confidence and skills. Speaking up, confronting, challenging and motivating others are all key skills you will gain from treating the classroom as a leadership experience. Some will be based on gaining skills not easily able to be ‘taught’, such as dealing with challenges, feeding back to team members, and presenting a professional image. How this paper will be taught Delivery Mode This paper will be offered in a FLEXI format where students can participate on-campus in Hamilton or online via Zoom synchronously. We expect students to participate in all sessions synchronously and some assessments may be scheduled at specific times. You are expected to participate fully in group work and assessments for you to be able to meet the requirements and expectations of this paper. All supportive online resources and class recordings will be available via Moodle. Purpose This paper is designed to identify and develop participants' leadership potential; to facilitate the process of ongoing personal and leadership development and to lead organisations effectively, particularly through change. It guides leaders and aspiring leaders through research and experiential practices on the role of leaders and their influence in today's changing and complex environments. Leadership is not a sole activity, so additionally we focus on the way leaders and followers interact, notions of team and shared leadership, and explore assumptions, beliefs, and values embedded and shaped in these practices. The purpose of the paper is to: Recognize and apply effective leadership strengths, attributes and skills, and develop a personalized leadership development plan. Understand, apply and critique changes in organisations and the role of leadership. Understand, apply and reflect on research and current perspectives aimed at enhancing leadership in organisations. Analyse, critique and apply shared leadership concepts and constraints. Experience virtual teams, virtual leadership, and change. What you will study Topic Introduction to the course and "The six lenses of Leadership". Lenses 1 & 2: Person and Position Lenses 1 & 2 continued Guest speaker Prof. Brad Jackson and Lens 3: Leadership through Process 5R Reflection (Individual assessment) 20% of overall grade Lens 4: Leadership through Performance Collaborative reading 1 (Individual assessment) 5% of overall grade Lens 5 and 6: Leadership through Place and through Purpose Collaborative reading 2 (Individual assessment) 5% of overall grade Group presentations Class presentations (Group assessment) 20% of overall grade Immunity to change part 1 Collaborative reading 3 (Individual assessment) 5% of overall grade Immunity to change part 2 Immunity to change part 3 Collaborative reading 4 (Individual assessment) 5% of overall grade Critique of change frameworks (In pairs) 20% of overall grade Course wrap up Immunity to Change Map (Individual assessment) 20% of overall grade
AS.440.617.80 : Financial Econometrics Course Information: Financial Econometrics [Time-Series Analysis] AS.440.617.80 ( 3.0 Credits ) AE Spring 2025 [AE Spring 2025] Description [formerly 440.647] This course introduces students to the methods most commonly used in empirical finance. Key models and methods are ARCH, GMM, Regime-Switching Models, test of CAPM (Capital Asset Pricing Model), term structure models, and volatility models (implied, stochastic volatility). Students will also learn aspects of time series econometrics for both stationary and non-stationary variables at different time frequencies, with emphasis on financial variables.Prerequisites: 440.601 Microeconomic Theory and Policy; 440.606 Econometrics; 440.614 Macroeconometrics is recommended.. What to Expect in this Course: This course is 15 weeks in length and includes individual, group, and whole group activities in a weekly cycle of instruction. Each week begins on a Tuesday and ends on the following Monday. Please review the course syllabus thoroughly to learn about specific course outcomes and requirements. Be sure to refer to the Checklist each week, which provides a week-at-a-glance and shows targeted dates for the completion of activities.
Homework 1 Part I: Basic Concepts 1. There are two vectors, x1 and x2 What is the distance between x1 and x2 ? (Please show the steps of the calculations) (1) if the distance measure is based on L2 norm (a.k.a Euclidean norm) (2) if the distance measure is based on L1 norm (3) if the distance measure is based on L∞ norm (a.k.ainfinity norm) In class, we studied the customer segmentation example and tried to find the most valuable customers who have good income but low spend. There are two feature components in this application. Assume that we use a clustering method similar to k-mean, and this method could use any type of vector norms as distance measure. Then, does the L∞ norm-based distance measure make sense for this application? 2. We define a scalar valued function of a vector variable Here,x is a column vector, xT is the transpose of x, and A is asymmetric matrix To simplify this question, let's assume x has only two elements and The derivative of f with respect to x is a vector defined by Show that dx/df = 2Ax Hint: calculate f(x), 2Ax, da/df and dβ/df K-means clustering (10 points) 3. Briefly describe the two key steps in one iteration of the k-means algorithm. (1 point) 4. What is the distance measure used ink-means (implemented in sk-learn)? (1 point) 5. The k-means algorithm can always converge in a finite number of iterations. Why? (1 point) 6. The clustering result of k-means could be random. Why? (1 point) 7. The minimum value of the loss function is zero for any dataset. What is the clustering result when the loss function is zero? - assuming that the dataset has millions of different samples. (1 point) Note: for questions 3,4,5,6,7, you only need to write a few words (bullet points) for each one. 8. find the optimal centers by following the steps below when cluster labels are given. (5 points) The loss function is as defined in the lecture notes. First, we calculate , where k could be 1, 2, 3, … , K. Then, we set and we obtain the optimal center What are (A), (B), (C), (D), and (E) in the above equations ? Note: (E) is a variable, not a word or sentence Part 2: Programming Complete the tasks in the files: H1P2T1_kmeans.ipynb If you want to get some bonus points, try this task: H1P2T2_kmeans_compression.ipynb Grading: the number of points The following rules are used for every homework assignment. Each homework assignment is an individual assignment, NOT a group assignment. For part 1: You may use MS-word to write the answers, convert the file to PDF, and upload it to Blackboard. You may write the answers on a piece of paper, take a photo using your cellphone, and upload the picture to Blackboard. Make sure that your handwriting is human/TA-readable, otherwise you may lose points. For part 2: complete the ipynb files. Do NOT convert ipynb files topdfor py or another format. Upload your files to Blackboard and do not miss any files. Before you submit homework files, make sure you run each and every code cell of your program files. If a code cell is supposed to generate some output (e.g., figure or text) and nothing shows up below the cell because you forget to run the cell, you will lose the points of that cell. Do NOT use ChatGPT and Copilot.
Foundation Studies ICFINF7000 Information Technology for Academic Purpose ICFINF7000 Project Part B 2024 Training Service Spreadsheet As in the Project part A instructions: “Case Study You are the manager of a Training Service business. You provide a service such as personal exercise training, cooking lessons, guitar lessons, car driving skills etc. You employ several trainers and care for over fifty clients. Your business takes place at various locations. You wish to manage the business so that you maintain the existing clients and gain new ones.” Spreadsheet (95%): You are to create a spreadsheet to record clients, activities, locations and training sessions data to aid in making business decisions. Below is a list of what must be included in the spreadsheet. The spreadsheet should include the following separate sheets as specified: Sheets: 1. Clients sheet A sheet to record client data. Include: a. Name sheet “Clients” b. Business name heading and logo (as per Project Part A) c. Appropriate client identity information including first and last names and a client identifier. Person names tend not to be unique, so introduce a client identifier. For example, students have a student number for unique identification. d. Client contact details. Consider what contact details are appropriate and required (considering privacy and security), street address? email? mobile? e. Client initial statistics i. Client health details. Consider what health details are required and appropriate. E.g. A personal training business with a goal for weight loss may record client’s initial height and weight. OR ii. Client starting skill level. E.g. A piano teaching business may wish to record the initialskill level such as beginner, intermediate or advanced OR iii. As required by your case study business f. Client personal details (allow client to not disclose this information if they wish): i. Gender ii. Birth Date iii. Age (this should be calculated and so changes overtime) g. Client Membership or Discount status. Use a business decision to decide if you will have membership or discounts or a status of your choice available to clients i. Type of status (Y/N) e.g. Member? ii. Status number if needed e.g. Member Number iii. Date Joined status e.g. Date Member Joined h. Populated with at least 50 clients including: i. Yourself as the 15th client, include your full name, other details can be made up. ii. Your teacher as the 20th client, include their full name, other details can be made up. 2. Activities sheet A sheet to record activity data. Include: a. Name sheet “Activities” b. Business name heading and logo (as per Project Part A) c. Activity identity details. Consider giving each training a unique code. d. Activity name and/or details e. Activity charge f. Any discounts applicable (members?) g. Populated with at least 10 activities. Examples: The personal training business, TrainTogether provide multiple activities for its clients to choose. For example, 1 hour group training sessions. Cost is $45 for members and $50 for non-members. TrainTogether also have private sessions. Cost is $80 for members and $100 for non-members for 1 hour. Cost is $60 for members and $80 for non- members for 30 minutes. The cooking class business Let’s Cook, holds 2 hour baking bread classes. Cost is $55 for non-members and $45 for members. They also have 1 hour cooking lessons for beginners. Cost is $45 for non-members and $35 for members. 3. Locations sheet A sheet to record activity location data. Include: a. Name sheet “Locations” b. Business name heading and logo (as per Project Part A) c. Locations with name and address and phone number d. Location size (square metres) e. Facilities available as required by your business f. Rent if any g. Restrictions if applicable (e.g. weather, closures) h. Populated with at least 5 locations Examples: The personal training business, TrainTogether uses the following two locations: Newcastle Training Centre is located at 181 Darby Street, Cooks Hill. (49482424). There are two 100 square metre training rooms available at $100 per hour. Facilities include weights, fitness machines, showers, toilets and coffee shop. The centre is unavailable on public holidays. Nobbys Beach. Facilities are sand and water training. Toilet, showers and coffee are available. No cost charge for groups of 10 or less people. It requires a council booking of $100 for groups between 10 and 100. No bookings for groups greater than 100. It is not a suitable venue for training when weather is wet or stormy. 4. Training sessions sheet A sheet to record client training sessions at locations. Include: a. Name sheet “Training sessions” b. Business name heading and logo (as per Project Part A) c. Training session details: i. Date ii. Time iii. Client details. Add data validation for the client identifier to provide a drop-down list to allow choice of the client identifier. Then use the client identifier and a function to display the client names and any other required client details (such as member status) from the Clients sheet. iv. Employee/sinvolved. v. Location. Add data validation using the valid data from the Locations sheet. vi. Activity details Use data validation and functions like part iii for the activity details from the Activities sheet. (1) Activity (2) Charge (with and without any applicable discounts) vii. Any recording of client health statistics or skill level d. Populated with at least 20 training sessions. e. Include at least 1 client with multiple training sessions. Examples: The personal training business, TrainTogether held these training sessions: Client Sue Jones attended a 1 hour group training session at Nobbys Beach on the 3rd of March 2024 at 10am. She was trained by Tom Smith. Cost was $40. Her weight was recorded at 62kgs and her resting heart rate at 65. Client Sue Jones attended Newcastle Training Centre on the 3rd of August 2024 at 3pm for a 1 hour private session. She was trained by Sally Marks. Cost was $80. Her weight was recorded at 60kgs and her resting heart rate at 63. Sue is a member and received a 10% discount for both sessions, 5. Client Training sessions sheet A sheet for one client from your Clients sheet showing all training sessions by that one client. These training sessions need to be already recorded on the Training sessions sheet. Include: a. Name sheet “Client Training sessions” b. Business name heading and logo (as per Project Part A) c. Client details. Add data validation for the client identifier to provide a drop-down list to allow choice of the client identifier. Then use the client identifier and a function to display the client names and contact details from the Clients sheet. d. Display all of one client’straining sessions from the Training sessions sheet. Ensure that if any changes occur on the Training sessions sheet the changes will also occur automatically on this sheet. e. Show the client’s total spend for the training sessions listed. f. Include some client analysis. E.g. For a personal training business highlight weight gain or loss. For a piano lesson business highlightskill level changes.
URBA6006 TsangNokSze 3035776660Evaluation of Climate Model – Bias and Uncertainty in Climate PredictionAcademicPaper–ClimateModelPaperTitle Model1 Quantitativeurbanclimatemappingbasedonageographical GIS-basedsimulationdatabase:AsimulationapproachusingHongKongasacase approach–MeansofSVFstudy(Chen&Ng,2011) andFADsimulation2 Applyingurbanclimatemodelinpredictionmode–evaluation MUKLIMO_3ofMUKLIMO_3modelperformanceforAustriancitiesbasedonthesummerperiodof2019(Hollósietal.,2021)3 Reanalysis-drivenclimatesimulationoverCORDEXNorth CandianRegionalClimateAmericadomainusingtheCanadianRegionalClimateModel, Modelversion5:modelperformanceevaluation(Martynovetal.,2013)4 Evaluationofextremeclimateeventsusingaregionalclimate RegionalClimateModelmodelforChina(Ji&Kang,2014) Version4.05 ExtremeclimateeventsinChina:IPCC-AR4modelevaluation RegionalClimateModel–andprojection(Jiangetal.,2011) IPCCAR46 Afutureclimatescenarioofregionalchangesinextreme PRECIS,aregionalclimateclimateeventsoverChinausingthePRECISclimatemodel modelsystem(Zhangetal.,2006)7 ClimatechangeinChinainthe21stcenturyassimulatedbya RegionalClimateModelhigh-resolutionregionalclimatemodel(Gaoetal.,2012) version3(RegCM3)8 AregionalclimatemodeldownscalingprojectionofChina RegionalClimateModelfutureclimatechange(Liu,Gao&Liang,2012) version3(RegCM3)9 ChangesinExtremeClimateEventsinChinaUnder1.5°C–4 RegionalClimateModel°CGlobalWarmingTargets:ProjectionsUsinganEnsembleof (RgCM4)RegionalClimateModelSimulations(Wuetal.,2020)10 ClimateChangeoverChinainthe21stCenturyas RegionalClimateModelSimulatedbyBCC_CSM1.1-RegCM4.0(Gao,Wang&Giorgi, (RgCM4)2013)IntroductionThe climate model is an extension of weather forecasting, it usually predicts how average conditionswill change in a region over the coming decades (Harper, 2018). To understand how to evaluate aclimate model, we should understand the components of a climate system. A Climate system is asystemcombiningtheatmosphere,ocean,cryosphereandbiota,therefore,therearelotsofparametersthatwillaffecttheclimatesituationofaregion.The climate model is usually used by researchers to understand complex earth systems. The modelinputs will be the past climate data which acts as a starting point for typical climate systems analysisand a model can be created and used to predict the future climatic situation as the model output.Therefore, the more we learn from the past and present climatic situation, the more accuracy of themodeltopredictthefutureclimaticsituation.Model accuracy and precision depended on the following three major parts, includingInput, which isrelated to the data quality and quantity; model which depended on the quality and quantity ofparameters,temporalandspatialextentsettings;andoutput,whichisabouttheaccuracyandprecisionoftheforecastingofthemodel.URBA6006 TsangNokSze 3035776660EvaluationA) ComplexityofmodelProblemofparametersThere are increasing statistical methods of multimode climate projections, the complexity of themodel in analyzing different parameters also hence to enhance to predict different possibilities of thefutureclimaticsituation. However,mostoftheresearchersmentionedinthispaperareonlyinterestedin ranking the importance of the different parameters in affecting and controlling the climate system.They will try to do some correlation between the parameters and the climate result to find whichparameters should be included in the climate model for prediction and analysis. However, what weneed to focus on is how these models predict the changes in the climate of the region, their ability topredict the accurate trends of the climatic situation. It is important to note the complexity of theclimatemodelisnotinalinearrelationshipwithitsaccuracyinpredictingfuturetrends.B) UncertaintyandBiasofthemodelThe uncertainty of the model causing overestimation and underestimation of the model in predictingthetemperatureandprecipitation.The issue of uncertainty and bias are the core parts of the climate change prediction problem. Due tothe complexity of these issues on both concept and speciality, uncertainty and bias will remain aninevitableissuesinthedebateofclimatechange.TheproblemoftopographyAs indicated by much research on climate models based in China, the problem of topography is themajor limitation for the collection of data in the first stage. China is known as a country withcomplicated topography, including mountains, basins, plateaus, hills, and plains. It is important tonote that complicated topography largely affects the climate models stability (Mesinger & Veljovic,2020), and this topography characteristic has been reviewed by Martynov et al. (2013), Jiang et al(2011)andZhangetal(2006)asthebarriersindatacollection.For example, as stated in research of Martynov et al (2013), the horizontal resolution in the climatesimulation is insufficient for such a complex topographical situation, while the vertical interpolationof the pressure gradient simulation is also affected by the complex topographical factors. Similar totheresults as statedintheresearchof Jianget al(2011),the complexityofthe topology inChina alsoaffect the accuracy of the model in predicting future precipitation, especially for the case oftopography-driven precipitation, the related data is not well measured and recorded by the coarseresolution model. Mountainous regions of China also induced bias issues. Some weather stationslocatedinthevalleyorlowelevationregionsmayalsoresultinthecoldbiasoftheclimatemodellingresults. As reviewed in the regional climate model in research of Zhang et al (2006), the operation ofcomplex topography in China with the strong monsoon system causing a large spatial variability inthepredictionaccuracyoftheclimatesystem.TheproblemofhumidityBoth humidity and temperature are the major components in the climate model while humidity haslong struggled in the climate models in whether it has been adequately represented the cloud systemsto tropospheric humidity in the calculation of the climate system. In the research done by Ji & Kang(2014), the factor of humidity in the formulation of climate systems becomes the greatest uncertaintyinclimatemodelprediction.TheclimatemodelstatedinJi&Kang(2014)researchalsoindicatedtherelative humidity prediction appears to be much less credible and show a large variety of modelpredictionskills.URBA6006 TsangNokSze 3035776660It is necessary to include a comprehensive analysis of the dynamic cloud processes so to evaluate thehumidityeffect inthe climate model. Moreover,humidityis highlyvariable over small scales of timeandspace,whichisahugeuncertaintyfortheregionalclimatemodel,thiswillleadtoalargerangeofpotential results in the future, directly affect the forecasting ability of the model. (Maslin & Austin,2012).TheavailabilityofobservationaldataClimate observations are used as a baseline for accessing climate changes. As revealed in someresearches, complicated topography that falls within a large range of elevation largely affect dataquality and quantities of climate data collected. For instance, the temperature and humidity relateddata are hardly collected. For example, for the Hollósi et al (2021) research on applying climatemodels for Austrian cities, the problem of uneven distribution of weather stations is found. In othercities of Austria, because of the limited number andsparsely placeddata collection stations, there aremuchlessobservationaldataofsome ruralregions.Evenifthecitieshavearelativelyhighamount ofweather stations, due to the building geometry differences between rural and urban citiesenvironmentalsetting,somepatternssuchasheatloadisnotproperlyinvestigatedandmonitored.Therefore, the quality and quantities of the observational data are not stable and reliable for someclimate modes, resulting in large uncertainties and difficulties when analysing the climatic differencebetweenurbanandruralareas.C) TheforecastingabilityofthemodelThe limited forecasting ability of the climate model is not inevitable. It is so hard to predict climatechanges, which highly depends on the data quality measured and captured by the measurementstationsorequipment(Maslin& Austin,2012).Also,ouratmosphericstructureis socomplicatedandthe climatic situation is affected by many external factors that cannot be analyzed and found out byonesingleclimaticmodel(Herrington,2019).TheproblemofusingpastclimaticdatainpredictingextremeweatherIt is important to note that climate has changed so extremely and intensely that the frequency of pastextreme eventsisnolongerareliablepredictor, especiallyforthehuman-inducedwarminghasontheextremeevents.Hence,theuseoftemporallylaggedperiodsofextremeeventsprobablywillprobablyunderestimatethehistoricalimpacts,andalsounderratetherisksoftheoccurrenceofextremeweather.As stated by Foley (2010), the technique that using historical observation data to calibrate futuremodel projections is not precise enough when the model is trying to simulate and validate a state ofthe system that has not been experienced before. This is an inevitable barrier for the modelcomputationsofthenaturalsystems.Researches done by Ji & Kang (2014), Jiang et al (2011) and Gao, Wang & Giorgi (2013) tries topredict extreme weather by using the historical data at different ranges, basically using the range ofthe temperature as the observational data as the input of the model. Sometimes the problem ofcomplicated topography of China will also induce large biases in the collection of climatic data,includes the daily mean temperature and the records minimum and maximum temperature. Asmentioned by Sillmann et. al., (2017), predicting extreme weather needed to depend on the presenceof large scale drivers, which should be the major contributors to the existence of extreme weather.Therefore, instead of using the separate dynamic and physical processes in the predictive model topredict climate changes as stated in research Ji & Kang (2014), Jiang et al (2011) and Gao, Wang &Giorgi (2013), the researches should focus on the interrelationship between the processes, a betterunderstandingof the processes canallowus torealize the underlyingdrivers of theresults of extremeweather.URBA6006 TsangNokSze 3035776660OverestimationandUnderestimationThe climate models overestimated the interannual variability of temperature. As indicated in the Ji &Kang(2014)research,thenetworkofprecipitationpatternsthatareprocessedfromstationsinthearidareas may underestimate the precipitation over the northern topography of China. While the Jiang etal (2011) research indicated the regional climate model tends to overestimate the precipitationsituationinthenorthernandwesternpartsofChinawhereintenseprecipitationisrarelyfound.Ontheother hand, the climate model also underestimatedthe precipitation that will exist in the southern andnortheastern parts of China in the future. A similar result was also found in the Zhang et al (2006)research,whichindicatedthattheclimatemodelunderestimatedtheexistenceofextremeprecipitationeventsinthesouthernpartofChina.For the climate model researches done in Hong Kong (Chen & Ng, 2011), only building geometry istakingintoconsiderationinclimatesimulation,bothtopographyandvegetationcoverarenotincluded,indicated that the results may overestimate the real temperature for the location located in higherelevationwithlargevegetationcover.LimitationoftheRegionalSimulationsinRegionalClimateModelMostoftheresearchesindicatedinthispaperfocusontheregionalclimatemodel,whichisthehigherresolution model compared to the global climate model. Therefore, with a finer resolution of theregional climate model, scientists can have a higher ability in resolving mesoscale phenomena thatcontributing to heavy precipitation (Jones, Murphy & Noguer, 1995). However, as the regionalclimate model onlycover certainparts ofthecontinental, thelateral boundaryconditionis requiredinthe model simulation. Therefore the accuracy of regional simulations is highly dependent on theboundaryconditions of the observations. When the regional climate model is affected by some cross-boundary external forcings, uncertainties must have easily existed when the climate model trying toforecastorprojectthefutureclimateinboundaryconditions.(CCSP,2008)ConclusionFormulation and using a climate model to analyze the climate data and making the prediction isbecoming a new trend for scientists and researchers to enhance our understandings of the earth welived on. With the increased complexity of the climate model, more and more factors are putting intoconsiderations when we trying to predict the climate situation. However, despite the climate modelare more sophisticated in today’s society, biases and uncertainties still existed, but we should alsoneedtounderstandthat there is noperfect modelwith nobias anduncertainty. As longas the climatemodelisabletoensureanddecidethesensitivityoftheactualclimatesystemtosmallexternaldrivers,theweightof scientificevidence isalreadyenoughtogive us the informationandmake anacceptablepredictionoftheclimaticsituationofourworld.
Module Code: CMT304 Module Title: Programming Paradigms Assessment Title: Quantum Computing Assignment Consider the following quantum circuit: It consists of two CNOT gates in the middle of the circuit. The two-qubit input quantum register |x〉is an arbitrary quantum state and can be set by the user. The other two-qubit input quantum register |00〉is in the ground state and cannot be changed. The gate F is an unknown quantum operation (this means it is an arbitrary, but fixed gate on two qubits, but you do not know what it does). The gate F −1 computes the inverse operation of F. 1. Analyse the operation of the circuit to determine what the values of the two two-qubit output quantum registers |A⟩ and |B⟩ are, depending on the properties of F and the user-selectable input |x⟩ . Clearly justify your answer. 2. Explain how you could, if possible, determine the operation of the gate F from this circuit (you can execute the circuit as many times as you wish). 3. Furthermore, discuss what this means for the difference between quantum comput- ing and a classical computing paradigm of your choice (working with bits instead of qubits). Answers should be provided in a report of up to 500 words (formulae and code do not count towards this limit, but ensure you explain any formula and code included). The word limit is an upper limit, not a target length. Text longer than the word limit may be ignored. Learning Outcomes Assessed • Explain the conceptual foundations, evaluate and apply various programming paradigms, such as logic, functional, scripting, filter-based programming, pattern matching and quantum computing, to solve practical problems. • Discuss and contrast the issues, features, design and concepts of a range of program- ming paradigms and languages to be able to select a suitable programming paradigm to solve a problem.
HPSC0004 Philosophy of Science 1 Syllabus 2024/25 Course Description This is an introductory module in the philosophy of science. The course is divided into two parts: (1) the epistemology of science and (2) the metaphysical issues in the sciences. The first part of the course will focus on several central problems regarding the nature of scientific knowledge: how do scientists know if current scientific theories are true? Is science progressive? How do scientists test their theories and how are theories confirmed? Can science and pseudoscience be distinguished? How are sciences distinguished from one another? These questions will be discussed in the light of examples from science. The second part will focus on the realism/anti-realism debate, the status of scientific theories, the laws of nature and causation. Towards the end of the course we will also consider some of the overlap between social and ethical issues and the sciences. During the course of discussing these problems, you will study some of the major positions that have been taken about scientific knowledge both in the history of philosophy and in the 20th century: Inductivism (Bacon),Logical Empiricism (Ayer and Quine), Falsificationism (Popper), Incommensurability (Kuhn) and Relativism (Feyerabend). Philosophy of Science 1 will provide you with the background knowledge that you will need for other Philosophy courses that you will take in later years. You do not need prior knowledge of philosophy or science to do this course. Assignments Assignments will take the form. of an a 2000-word essay on a set question and a 2-hour in person unseen exam. Each assignment will constitute 50% of the credit for the module. Essay questions and instructions will be distributed within the first three weeks of teaching. Lecture time will be designated to assisting students with writing philosophical essays. The unseen exam will mirror the taught content, with each question based on a weekly topic. The unseen exam will be two hours in length, with students needing to answer three questions. There will be an exam preparation session in the early part of term 3 to assist students in their preparation for the exam. Aims and Objectives Aims To teach students about the foundational thinkers and topics in 20th century philosophy of science. To provide students with a foundation in the philosophy of science required for further study in years 2 and 3. To teach students about some of the more recent conceptual and disciplinary shifts within the philosophy of science that have occurred in the early part of the 21st century. To promote thinking through theory using concrete, real world examples. Theoretical concepts will be grounded in case studies from scientific practice and the interplay between science and wider society. To integrate topics covered in the module with related theoretical concepts from other courses available within the Department of Science and Technology Studies. Objectives By the end of this module students should be able to: Evaluate the key philosophical accounts of many core topics inthe philosophy of science. Write philosophically coherent essays, where philosophical theories areexplained and arguments for them critically evaluated. Ground theoretical views in real world cases drawn from the history of science and contemporary science. Think philosophically about the core topics, analysing arguments critically, consider opposing views fairly and philosophically justify their own. Integrate the philosophical concepts learnt on this course with other HPS, STS and Philosophy courses.
HPSC0010 History of Modern Science COURSE DESCRIPTION Why do some ideas change the world, while others never get off the ground? Why do some policies transform. lives for the better, while others only cause more harm? What if future generations had a way to identify problems before damage is done or before great ideas are wasted? Critical study of the history of science, its successes and its failures, can provide the answers, and make sense of our present to help develop better futures. In HPSC0010: History of Modern Science, we explore the development of science, technology, mathematics and medicine from the late 18th Century to the present; look critically at the different ways in which past societies understood the world and how it works. We study the complicated relations between scientific, popular, and religious views of the world; and we explore how some social movements have been fundamental in advancing scientific progress while other ideologies have driven exclusion, misinformation, and abuse. WHAT DO WE EXPECT FROM YOU ON THIS MODULE? • To attend lectures and tutorial seminars, and ensure your attendance is registered. • To notify the course tutor, [email protected], if for any reason you are unable to attend. • To complete the required preparation before the relevant tutorial seminar. • To actively contribute to discussion in lectures and tutorial seminars. • To read and follow the assessment instructions, including those related to submission. • To contact [email protected] as soon as any issues arise. WHAT CAN YOU EXPECT FROM US ON THIS MODULE? • Support to develop informed historical perspectives on the history of modern science and its relevance to urgent present-day issues. • A practical introduction to cutting-edge approaches and methodologies, as well as some of the biggest ideas in the field from the past 50 years. • Weekly opportunity to discuss your questions and insights both with the lecturer and the seminar tutors. • Guidance to get the marks you deserve in assessments. • Detailed feedback on your assessments to support your future work and further enhance your skills. HOW WILL THIS MODULE BE TAUGHT? • This module is taught as a combination of lecture; post-lecture discussion; tutorial seminar; and independent study in preparation for the tutorial seminar and assessments. • Post-lecture discussion provides an informal opportunity to discuss your thoughts and chat about ideas with peers and with the lecturer. • Independent study will usually take the form. of planning responses to questions using examples from the lecture and an essential reading. Optional further readings are also provided. • Tutorial seminars provide an opportunity to talk through your planned question responses and get feedback that will help you get the marks you deserve in assessments. ASSESSMENT WHAT IS THE ASSESSMENT? • The assessment is two short coursework essays. • Essay 1: 1,000 words. • Essay 2: 2,000 words. WHEN ARE THE DEADLINES? • Essay 1: 24 March 2025. • Essay 2: 21 April 2025.
HPSC0003: History of Science, Antiquity to Enlightenment Course Syllabus 2024-2025 Course Information Surveys the origins and development of science from the ancient Greeks to 1800. Main themes are the origins of science in the ancient world, the nature of the Scientific Revolution and the spread of science during the Enlightenment. ASSESSMENT: ESSAY 1 Write a critical analysis of one of the essential readings from classes before reading week. This should take the form. of an essay of no less than 1400 and no more than 1500 words, excluding bibliography. What do you need to do? People often think that history books give us “the facts” – unassailable information about the past. But historical texts are a representation of events that inevitably include some things and leave out others. A critical analysis of a text will identify the arguments being made by an author and consider their merits. Questions to be explored may include: • Who is the author of this text? • What is the geographical and temporal scope of this text? • What is the topic of the text?/what themes does it explore? • What is the author’s overall argument? • What sections does it have? What does each section argue? • Do you think the author is successful in making their argument? Have they presented a convincing case? • What evidence does the author use to support their claims? (examples of primary and secondary sources) Is there evidence that might challenge their argument? • What have other authors on the syllabus said about this topic? What are the possible contrary arguments? • Is there anything that the author has overlooked? • What avenues are there for further research? Essays should address these questions and provide some depth in explaining the author’s arguments. When answering, avoid speculation – a speculative answer is one that does not have any evidence to support it. You should always be able to point to a word or passage in the text that supports your interpretations, so use brief quotations (one or two sentences, not one or two words) to support your points. Please read the STS Student Handbook for advice on late penalties. Essays should only make use of the assigned literature. ASSESSMENT: ESSAY 2 You are required to write an essay of no less than 1400 and no more than 1500 words. This should be another critical analysis of an essential reading, this time from classes after reading week. The same terms apply to this essay as the essay in assessment 1. Criteria for assessment The departmental marking guidelines for individual items of assessment can be found in the STS Student Handbook. In addition to the criteria indicated in the STS Student Handbook, the following are the main criteria on which your research essay will be marked. There are no set numbers/percentages associated with these criteria but we will give you qualitative feedback based on them. Referencing You must reference all quotes and all references/ summaries of books, etc. Pick one system for referencing and stick to it. Refer to individual page numbers, not just whole texts, whenever possible. Make sure you are clear what plagiarism means and do not plagiarize in the essay. Bibliography You need to supply a bibliography of all works referenced. You must supply author, title, date, place of publication and publisher. Essays should only make use of the readings given in the syllabus. Organisation Is the essay organized into an introduction, main body and conclusion? Does each part flow naturally into the next one? Is the evidence presented in a logical order? Introduction You should give an introduction to your essay in one or two paragraphs. Introduce your topic and your line of argument, no more. Good introductions are concise. Clarity We place great emphasis on clarity of argument and expression. Avoid ambiguity and vagueness. Explain anything that might not be obvious. Do not assume your reader already knows what you are talking about. Try to keep your line of argument clear. Accurate spelling, grammar, and punctuation also improve clarity. Argumentation Is the main argument of the essay clear, coherent and persuasive? Is it properly supported by the evidence available? Conclusion Your essay should have a conclusion (typically one paragraph) which is clearly marked as such (new paragraph, ‘In conclusion…’). It should sum up what you have argued and explore the implications of what you have argued. Reading/ use of sources How well have the readings and other resources been used? Does the essay reflect them accurately? Is the essay overly dependent on one source? It is recommended that you use two or three other readings from the syllabus to develop your critique. Avoid just mentioning them – explain the relevant arguments made by each author. Independent critique? Does the essay offer some independent critique or thought on the question or does it merely report what is in the literature? Historiography? How aware is the essay of assumptions and methods used to construct a history or to evaluate it? Does the essay discuss what historians have said about the topic and offer some critique of them? Aim of the course The general aim of the course is to present an overview of the History of Science from its ancient beginnings up to the end of the eighteenth century and to begin to offer critical perspectives on this history. The course does not require any technical knowledge of current science. Students will become familiar with the history of science from antiquity to 1800 in Europe and other parts of the world. The course offers critical appraisal of the ways historians have told this history. The course provides a foundation for further modules in the second and third years of the degree which explore issues around the history of science in more depth. Objectives of the course By the end of the course, it is hoped that you will have acquired : * a working knowledge of the history of science up to 1800 * an in-depth knowledge of elements of this history, demonstrated in essay assessments. * key critical writing skills; the ability to select the most important facts, to marshal those in argument and an awareness of the strengths and weaknesses of that argument. * some basic historiographical skills; an awareness of anachronism and the basic methods of writing the history of science.
HPSC0011 STS Perspectives on Big Problems Course Syllabus 2024-2025 Course Information This module introduces students to the uses of STS in solving big problems in the contemporary world. Each year staff from across the spectrum of STS disciplines – History, Philosophy, Sociology and Politics of Science – come together to teach students how different perspectives can shed light on issues ranging from climate change to nuclear war, private healthcare to plastic pollution. Students will develop research and writing skills. This year’s topic is: The State of the Oceans The UN has declared 2021 -2030 the Ocean Decade. The slogan is ‘the science we need for the Ocean we want’. Implicit in this statement is the idea that the Ocean is a realm that can be made to suit humanity’s needs and preferences through scientific knowledge production. Many scientists acknowledge that the ocean remains understudied, and there is still much left to discover in terms of ocean life and ocean processes. There is the also potential for the development of new materials from undiscovered resources such as the polymetallic nodules found on the ocean floor. But the science of the ocean extends from its depths, upwards, to the land and sky. It is implicated the stability of the atmosphere and climatic and weather patterns. In days past, the ocean facilitated the Age of Discovery, when nations developed the capacity to ferry men and women to the ‘new world’, both in the interest of exploration and later forcefully, with the goal of exploiting them for labour. Mercantilism and colonialism and the history of shipping and oceanography co-evolved hand in hand. Today, the seas hold the undersea cables that allow global, digital connectivity, facilitating a new form. of trade route and cultural exchange. The STS1Book this year illustrates the concept of ‘mutual shaping’--that the ocean shapes human society and the technologies that we build, and that our social norms, power dynamics and technologies impact the ocean in turn. Aims & objectives To demonstrate and explore the ways that STS provides perspective that contribute to the understanding of major problems facing humanity. Objectives: • The possession of empirical and theoretical knowledge of big problems from interdisciplinary STS perspectives, and the written communication skills to account for such knowledge • The skills to analyse and contribute to such knowledge • A deeper grasp of the varied character of STS and its interdisciplinary relevance to a wider world Assessment 1 (25%) ESSAY PLAN (assignment 1) Key info: Word limit: 1000 words (as per the STS handbook, you have a 10% margin, which here means 900-1100 words) Deadline: 27 November 2024, 5 pm. The purpose of assignment 1 is to produce some “building blocks” which will be useful to you in writing the final essay (assignment 2). It is therefore essential to first understand what you will be asked to do for the final essay. In a nutshell: • Your final assignment (#2) will be to summarise one of the topics presented over the weeks of the class and to explain the STS concepts, and readings that were discussed in the class. You will also be expected to include and engage readings that were not assigned to you. • This assignment (#1) consists in identifying the topic that you have selected, identifying an STS concept, and identifying reading(s) that you will be incorporating into your essay #2. The purpose of this assignment: this is an opportunity to practice and get feedback on some of the skills and “pieces” you will need for your final essay. Assessment 2 (75%): Essay 1)FINAL ESSAY (assignment 2): Key info: 2000 words, due 8 January 2025, 5pm. Word count margin: 1800 – 2200 words Your task in this essay is to summarise a topic discussed during one of the sessions. In the main part of your essay you should: • Identify the topic. • Explain your interest in the topic. • Include the STS concepts or ideas that were introduced along with the topic. Explain what they mean and how they are related. • Use at least two module essential readings, and at least one relevant reading that you have found on your own and reference these appropriately. You may also draw on lecture content and on media items such as newspaper articles, documentaries, commentaries, etc.
553.420/620 Probability Assignment #08 1. Consider the jointly continuous rvs X and Y with joint pdf f(x, y) = xe−x(1+y) for x > 0 and y > 0; f(x, y) = 0 elsewhere. (a) Compute P(Y ≤ 1|X ≤ 1). (b) Compute P(Y ≤ 1|X = 1). 2. A machine makes random rectangles. The length (X) and width (Y ) are independent random variables: X ∼ uniform(0, 1), Y ∼ uniform(0, 1). (a) What proportion of rectangles have area greater than 1/2? (b) Derive the pdf of A = XY , i.e., the area of a rectangle. Use the CDF method. (c)** What proportion of rectangles having area = 1/2 have length greater than 3/4? **For part (c), you will need to find the conditional pdf of X|A, this requires the joint pdf of X and A. This may require you use the method of Jacobians (take U = X, V = XY =⇒ X = U, Y = V /U). 3. Use the method of convolutions to show that the sum of two independent geom(p) rvs follows a neg.binom(2, p) distribution. 4. Suppose X ∼ uniform(0, 1) and Y ∼ uniform(0, 2) are independent. Use the method of convolutions to construct the PDF of X + Y . 5. (a sum of independent normals is normal) Let X1, X2, . . . , Xn be independent and, for each i, Xi ∼ N(µi , σi 2 ). Use the MGF method to show that ∑ni=1 Xi has a normal distribution and identify the mean and the variance of this normal distribution. Remark 1. The result of this problem is very important to remember (especially for the sequel course). Remark 2. You should think about what this problem says in the i.i.d. case, i.e., when all the normal Xi ’s have the same parameters, say µ, σ2 . 6. Let N be the number of customers that enter a facility. Suppose that N ∼ Poisson(λ). Let X be the number of customers that don’t buy anything while in the facility. Assume that given N = n, X ∼ binom(n, p). (a) Derive the (unconditional) distribution of X and identify it if you can. (b) Compute P(X = 0). 7. A person shows up to work X hours after 12:00PM (time 0), where X ∼ uniform(0, 4). If they arrive at time X, they work an amount of time Y that has an exponential distribution with parameter 5 − X. What’s the probability they are still working after time 8? 8. Suppose Y |X = x ∼ Exp(x) and X ∼ Gamma(α, 1). (a) Write down the PDF’s that are given to you in the problem statement. (b) Write down the joint PDF of X, Y . (c) Derive the (marginal) distribution of Y . If this distribution has a name, name it. Be specific. (d) Derive the conditional PDF of X given Y = y. If this distribution has a name, name it. Be specific. 9. Suppose Y ∼ uniform(0, X), where X follows the gamma density fX(x) = xe−x for x > 0. (a) Derive the PDF of Y . Identify the distribution of Y . (b) Let U = Y and V = X − Y . Construct the joint PDF of U and V using method of Jacobians. 10. Let X ∼ χ 2 m and Y = χ 2 n be independent. Let U = X/m Y /n = m n X Y . Derive the PDF of U. The distribution of U is called the F-distribution with m numerator degrees of freedom and n denominator degrees of freedom. Remark. To use the method of Jacobians you’ll need to choose a V that makes the transformation (x, y) 7→ (u, v) one-to-one. Although any such choice will lead to a correct marginal, I suggest V = Y because it might makes calculations more straightforward. 11. Suppose X and Y are random variables having the joint PDF fX,Y (x, y) = 4xy for 0 < x < 1, 0 < y < 1. Let U = X2 and V = XY . Derive the joint PDF of U, V . 12. X and Y have the joint pdf fX,Y (x, y) = e −y for 0 < x < y < ∞ (= 0 otherwise). Use the method of Jacobians to find the pdf of U = Y − X.
HPSC0009 Introduction to History, Philosophy and Social Studies of Science Course Syllabus 2024-25 This course is an introduction to history, philosophy, and social studies of science. We will think critically about key questions that have shaped, and continue to shape, this exciting and dynamic field of study. What grants the authority of science in our society? How have scientists constructed and maintained their identity through time, and has this come at the expenses of other social groups? What are the relationships between science, society and culture, and how have those relationships changed through time? What is the role of scientific experts in society? Should science today be a force behind positive social change, and if so how can we make it happen? Using historical and contemporary case studies, the focus of this module is to encourage students to start thinking critically about these questions, while at the same time developing their skills as independent, interdisciplinary and publicly engaged scholars. This course is intended as a foundation and sampler for later courses in Science and Technology Studies. How this module works This course is an introduction to History, Philosophy and Social Studies of Science, which aims at building key skills: reading and studying skills, locating bibliographical sources, referencing, argumentation/critical thinking, and oral and written communication skills. You will need these skills throughout your degree and they will be required in all modules in STS – but they will also be useful in your future professional life! Combining content and skill-building, you will have the opportunity to explore the field and acquire foundational concepts and methods to pursue further study in STS. The lectures and seminars take place in person on Mondays (please consult your timetable for the lecture venue and your allocated seminar slot). Attendance is mandatory, and there will be no recordings of the lectures and seminars. The lecture will cover the course material assigned for each week and explain the key concepts covered each week. The seminars will start with 15-20 minutes discussing your understanding of the readings, and you will be expected to contribute to the discussion. The remaining portion of the seminars will include activities and short group exercises aimed at developing studying, referencing, argumentation and critical skills. It is crucial that you attend both lectures (one hour per week) and seminars (one hour per week) if you want to do well on this course. Please familiarise yourself with the syllabus and with the Moodle page for this module. Make a note of the deadlines for each of the three assessments (detailed assessment instructions are also on Moodle, in the ‘Assessment’ tab). You will see that the Moodle page is organised in weekly topics. Each topic contains the activities you are expected to engage in each week. It also contains a list of links with the online resources (readings, videos, additional resources) that we will use in the module. Each week you are expected to complete the assigned readings (from beginning to end!), attend the lecture and seminars, and consult some additional materials which will help you understand the topic and clarify core concepts. You are also expected to use the UCL Library to locate additional literature that will help you gain a deeper understanding of the topics discussed each week (library skills will also be covered in the lectures and seminars). It is crucial that you complete the readings and engage in the skill-building activities in the seminars, as they are specifically aimed at helping you develop studying, referencing, and argumentation skills, build toward each of the three assessments, and discuss the course material and assessment with your peers. Coursework All the coursework for this module is tailored around developing studying, writing, research and argumentation skills. You will build toward your final essay in steps, with each part of the assessment helping you develop the skills you need to construct a clear, critical and well supported argument. You will start by learning the basics: how to locate, read, and annotate your sources. You will then move on to academic writing, starting with a draft plan of the essay you have chosen to write for this course among the suggested essay topics (Assessment 1). You will receive feedback from your tutors prior to the submission of the final essay at the end of term. You will then test your argument by presenting it briefly in an oral form. to your peers, and give your peers feedback on their own work (Assessment 2). With feedback on your plan from your tutors, and oral feedback from your peers, you will then be ready to complete and submit your final essay (Assessment 3) Detailed instructions on each assessment component are available on Moodle, in the Assessment section. Note that if you want to do well on the assessment you need to engage with the skill activities in the seminars group each week. These are geared toward building your skills gradually, and in parallel with the contents covered in each lecture. Criteria for assessment The departmental marking guidelines for individual items of assessment can be found in the STS Student Handbook. Criteria for marking are also explained in each Assessment Guidelines document, and will be discussed in class. Please note that the assessment for this course falls under Category 1 in UCL’s guidelines on using AI in assessment: AI tools cannot be used to complete it. More information, and the pedagogical rationale for this, are in the guidelines for each assessment in Moodle. Aims and Objectives Aims The aim of this course is to provide students with an overview of foundational concepts, debates and methodologies in the field of Science and Technology Studies. Combining content and skill-building, the course will equip students with conceptual and methodological foundations to pursue further studies in history, philosophy, and social studies of science. Learning Objectives and Outcomes On successful completion of this course students should be able to: 1. Understand and apply fundamental concepts in History, Philosophy and Social Studies of Science; 2. Locate sources in libraries and archives, and reference them consistently; 3. Analyse a scholarly text, identifying and assessing its key thesis; 4. Research independently, locating literature and case studies and evaluating their relevance in relation to a specific research question; 5. Build a sound argument, justifying its main claims through evidence from the literature; 6. Test the validity and limitations of HPS/STS concepts against independently researched historical or contemporary case studies
FN3142 Quantitative Finance Summer 2021 Question 1 Denote the price process of Bitcoin by P , and consider (T + 1) consecutive end-of-year price observations denoted by P0 , P1, ..., PT . Denote the simple net return series by and the logarithmic return series by rt ≡ log Pt - log Pt-1 for t = 1, ..., T. Assume that returns are independently and identically distributed over time. (a) [15 marks] Under the assumption that Bitcoin’s annual logarithmic returns are normally distributed with a mean of μ and a variance of σ 2 , derive a formula for the diference between the log expected simple gross return and the expected log return: log (E [1 + Rt]) - E [rt] (b) Consider the standard average estimator of the mean rate of return. Show that this estimator is unbiased in the sense that E[μ-] = μ, and derive its standard deviation, σ[μ-], as a function of the model parameters. (c) [15 marks] Assume instead that you observe Bitcoin prices more frequently, in particular N times per year (at equal distance from each other) for T years; for example, monthly ob- servations would mean N = 12. Consider now the simple average estimator of the annualised log return μ based on these N × T return observations, and let us denote it by ˜(μ) . Show that the standard deviation of this estimator, σ[˜(μ)], does not depend on the frequency N. (d) [20 marks] Suppose that a researcher tells you that for a given choice of N and T she estimated the annualised mean Bitcoin return to be ˜(μ) = 10%. Suppose also that the annualised volatility of Bitcoin log returns is known to be σ = 45%. What choice of T would imply that her estimate has a standard deviation of σ[˜(μ)] = 1%, i.e., one-tenth the size of the mean estimate? Discuss whether it is possible to have confidence in the rate of return of Bitcoin with reasonable accuracy given the available historical data. Let us now assume that annual log Bitcoin returns have a non-zero autocorrelation at lag 1 denoted by parameter ρ, but beyond lag 1 there is zero autocorrelation. (e) [15 marks] Derive E[μ] and σ[μ-] under this assumption, where μ refers to the estimator in part (b). (f) [15 marks] Discuss how a non-zero ρ afects your conclusion for part (d). Question 2 Consider the following AR(2) process: zt = Q0 + Q1 zt-1 + Q2 zt-2 + εt , (1) where εt isa zero-mean white noise process with variance σ2 , and assume j Q1 j , j Q2 j , j Q1 +Q2 j
