Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH206
Module Title: Statistical Distribution Theory
Module Level: Level 2
Module Credits: 5.00
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: MTH104 MTH113

 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.H. Understand statistical inference including estimation and hypothesis testing
 Method of teaching and learning This module will be delivered by a combination of formal lectures and tutorials.
 Syllabus Elements of probabilistic modeling Sample spaces, probabilities and conditional probabilities. Multiplication rule, total probability rule, and Bayes rule.Discrete random variables Discrete random variables and its probability mass functions, expectation, variance, functions of a discrete random variable, common discrete distributions: Bernoulli, binomial, geometric, Poisson and negative binomial distributions.Continuous random variables Continuous random variables and its distribution functions and density functions, expectation and variance, functions of a continuous random variable, common continuous distributions: uniform, normal, exponential, gamma, beta distributions. Multivariate random variables Joint distributions, marginal distributions, conditional distributions, covariance and its properties, conditional expectation, independence of random variables, functions of multivariate random variables. Moment generating functions. Central Limit Theorem. Convergence in probability and in distribution. The derivation of the chi-square, t, and F distribution.Point EstimationMaximum likelihood estimation, method of moments, sufficient statistics, Rao-Cramer lower bound, Bayesian estimation.Interval estimation Confidence interval estimation of population mean, proportion, difference of two means and difference of two proportions. Sample size determination. Resampling method.Hypothesis testing Hypothesis tests. Type I and Type II errors. P-values. Power of a statistical test. Applications to both single parameter and bi-parameter cases. Neyman-Pearson Lemma and likelihood ratio tests.
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark 1 Final Exam 70.00 2 Coursework 1 15.00 3 Coursework 2 15.00
 Module Catalogue generated from SITS CUT-OFF: 12/9/2019 11:39:04 PM