Elements of Probability and Statistics

Topic outline

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  General

  ELEMENTS OF PROBABILITY AND STATISTICS

  Instructor: Ceylan YOZGATLIGİL Added: 15 March 2010

  • Syllabus File
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  Topic 1

  Introduction

  Probability Axioms, Combinatorics

  • Lecture Note File
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  Topic 2

  Conditional Probability and Bayes Theorem

  • Lecture Note File
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  Topic 3

  Random Variables,  Expectation, Transformation (3 weeks)

  Random variables, probability mass function, probability density function, cumulative distribution function and their properties. Expectations of random variables, Transformations of variables, Parameter, Statistics, Measure of location, measure of variability, Box-Plot graphs, Covariance and Correlation.

  • Lecture Note File
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  Topic 6

  Mgf and Distributions (2 weeks)

  Moment generating functions, Statistical Distributions: Discrete distributions and their properties, Continuous distributions and their properties.

  • Lecture Note File
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  Topic 8

  Limiting Distributions & Sampling Distributions

  • Lecture Note 1 File
  • Lecture Note 2 File
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  Topic 9

  Point Estimation (3 weeks) 

  Maximum likelihood estimation, Method of moments. Unbiased estimators, Consistent estimators, Mean-square error, Sufficiency; Completeness, Rao-Blackwell Theorem, Complete sufficient statistics, Lehmann-Scheffe theorem, Minimum variance unbiased estimators, Exponential families, Fisher information, Rao-Cramer inequality, Efficient estimators, Asymptotic efficiency.

  • Lecture Note File
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  Topic 12

  Estimation II (2 weeks)

  Testing hypotheses: concepts of hypothesis testing, Neyman-Pearson lemma, Likelihood ratio test, Confidence intervals

  • Lecture Note File
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  Topic 13

  Distribution Fitting

  • Lecture Note File
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  Topic 14

  Simple Linear Regression

  • Lecture Note File