Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title STATISTICS AND PROBABILITY II
Code MATH254
Coordinator Dr L Yuan
Mathematical Sciences
Linglong.Yuan@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2024-25 Level 5 FHEQ Second Semester 15

Aims

To introduce statistical distribution theory which forms the basis for all applications of statistics, and for further statistical theory.

Learning Outcomes

(LO1) To have an understanding of basic probability calculus.

(LO2) To have an understanding of a range of techniques for solving real life problems of probabilistic nature.

(S1) Problem solving skills

(S2) Numeracy

Syllabus
 

1. Events, probabilities, random variables, distribution functions, probability density functions, discrete and continuous random variables, independence. Mean, variance and moments of random variables. Functions of a random variable. Some commonly used distributions: Binomial and Negative Binomial, Weibull, Normal, Log-Normal Normal, Gamma distributions. Special distributions in statistics: Chi-squared, t, F distributions.

2. Multivariate random variables: Joint, marginal and conditional distribution functions, Conditional expectations. Covariance of random variables. Bivariate Normal distribution and independence of bivariate Gaussian random variables.

3. Transformations of random variables: Use of direct methods and generating functions. Sum and ratio of two random variables.

4. Generating functions: moment and probability generating functions. Central limit theorem. Approximations. As illustrations of motivation by practical examples: Chi-squared etc.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
final assessment There is a resit opportunity. This is an anonymous assessment.  120    70       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Class Test  0    30