Statistics I
Course category:
2nd year
Module code:
MAT00010I
Year:
2012/13
Term:
Autumn
Credits:
10
Lecturer:
Dr Samer A Kharroubi AimsThe aim of the module is to extend your knowledge of statistical theory and its applications to introduce you to some of the basic methods of statistical inference and estimation, which are needed in data analysis. The aim will be achieved through a mixture of theory and practice. Learning objectivesAt the end of the module you should be able to...
SyllabusBackground. Probability, random variables and probability distributions, moment generating function and transformations of random variable. Joint distributions. Discrete and continuous random variables, conditional distributions, expectation and variance, conditional expectations and transformations of random variables. Bivariate normal distribution, chisquare, t and Fdistributions. Limit theorems. Modes of convergence (in distribution, in probability, almost surely), Central Limit Theorem, Weak Law of Large Numbers, Strong Law of Large Numbers. Estimation of parameters. Point estimation: generalities. Unbiased and consistent estimators, MSE distance, efficient and sufficient estimators, Factorisation Theorem, the method of moments, the method of maximum likelihood, CramerRao bound, efficiency of ML estimators under Gaussianity. Recommended textsStudents should obtain copies of the following tables:
Teaching
AssessmentOne and a half hour closed examination in week 1 Spring Term. Elective informationIntroduction to distributions arising in inference from normally distributed samples (and some others). Central limit theorem. Sample mean and variance. Please check prerequisites carefully before asking to take this module as an elective. In choosing this module as an elective it will be assumed that you are familiar with all the material taught in the first year courses Calculus and Core Algebra, or are willing to learn the material if necessary. Prerequisites


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