Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MTH206
Module Title: Statistical Distribution Theory
Module Level: Level 2
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: MTH104MTH113
   
Aims
This module aims to cement a solid foundation in the theoretical teaching of different statistical distributions and their applications. It provides an unusually comprehensive depth and breadth of coverage and reflects the latest in statistical thinking and current practices. This is a required module for students in a variety of fields in finance, economics, financial mathematics, natural sciences and engineering, etc. The designer/instructor of this module believes it is helpful for students to spend some time learning how the mathematical ideas of statistics carry over into the world of practical applications.
Learning outcomes 
A. Work with probability distributions, probability densities and multivariate distributions.

B. Calculate the expectation of a random variable.

C. Use moment generating functions to calculate the moments of a random variable.

D. Perform calculations with special discrete probability distributions, including binomial, geometric, and Poisson distributions.

E. Perform calculations with special continuous probability distributions, including normal, exponential and gamma distributions.

F. Find the probability distribution of a function of random variables.

G. Understand sampling distributions and the Central Limit Theorem.
Method of teaching and learning 
This module will be delivered by a combination of formal lectures and tutorials.
Syllabus 
Law of large numbers and Central Limit Theorem


Sum and quotient of random variables; functions of random variables; expectation of function of random vector.



Transformation of random vectors



Univariate, bivariate, multivariate RV, multivariate distributions




MGF, PGF



Joint distributions; marginal distributions; marginal density; conditional distributions; conditional density; conditional probability and independence; law of total probability; Bayes' rule; Pdf, pmf, cumulative distribution functions

independence of random variables; conditional expectation; law of total expectation; covariance and correlation; bivariate normal distribution



joint probability distribution; joint distribution function; joint pdf; joint conditional distribution;



joint conditional density; joint cumulative distribution, joint pdf



Weibull, Pareto


Simulation of random variables; The inverse transformation method. Random numbers from a normal and exponential distribution. Random numbers from Poisson and other discrete distributions. Rejection Sampling. Markov Chain Monte Carlo;


convergence of random variables in distributions of probability


chi-squared distribution, t-distribution, F-distribution

Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester              

Assessment

Sequence Method % of Final Mark

Module Catalogue generated from SITS CUT-OFF: 8/20/2019 6:20:18 PM