MA10212: Probability & statistics 1B
[Page last updated: 03 August 2022]
Academic Year:  2022/23 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Certificate (FHEQ level 4) 
Period: 

Assessment Summary:  CW 25%, EX 75% 
Assessment Detail: 

Supplementary Assessment: 

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

Notes:
