MA10212: Probability & statistics 1B

[Page last updated: 03 August 2022]

Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 2
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework 1 (CW 6%)
• Coursework 2 (CW 6%)
• Coursework 3 (CW 6%)
• Coursework 4 (CW 7%)
• Examination (EX 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA10211
Learning Outcomes: After taking this unit the students should be able to:
* Solve a variety of problems and compute common quantities relating to continuous random variables, including the use of joint probability density and distribution functions.
* Formulate, fit and assess some statistical models.
* Use the R statistical package for simulation and data exploration.

Aims: To continue the study of continuous random variables with a focus on the dependency of random variables. To introduce statistical modelling and parameter estimation and to discuss the role of statistical computing.

Skills: Numeracy T/F A
Problem Solving T/F A
Data Analysis T/F A
Information Technology T/F A
Written and Spoken Communication F (in tutorials).

Content: Advanced properties of continuous random variables. Properties of common continuous distributions including uniform, exponential, normal and gamma.
Transformations of RVs. Proof of the law of the unconscious statistician for a continuous RV.
Joint probability density functions. Marginal and conditional distributions of continuous RVs.
Independence: factorisation of joint PDF as a product of marginals. Properties of covariance and correlation.
Distribution of a sum of continuous RVs, including normal and exponential examples. Statement and application of the central limit theorem.
Introduction to model fitting. Exploratory data analysis and model formulation.
Parameter estimation by the method of moments and maximum likelihood.
Estimators as random variables. Sampling distributions of estimators. Bias, variance and mean square error of an estimator.
Graphical assessment of goodness of fit.

Programme availability:

MA10212 is Compulsory on the following programmes:

Department of Economics
• UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 1)
• UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
• UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
• UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 1)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 1)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 1)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
• USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 1)
• USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 1)
• USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 1)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 1)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)

 Notes: This unit catalogue is applicable for the 2022/23 academic year only. Students continuing their studies into 2023/24 and beyond should not assume that this unit will be available in future years in the format displayed here for 2022/23. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Find out more about these and other important University terms and conditions here.