Topic outline

  • General


    Photo of Ceylan Yozgatligil

    Instructor: Ceylan YOZGATLIGİL

    Added: 15 March 2010

  • Topic 1


    Probability Axioms, Combinatorics

  • Topic 2

    Conditional Probability and Bayes Theorem

  • 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.

  • Topic 6

    Mgf and Distributions (2 weeks)

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

  • Topic 8

    Limiting Distributions & Sampling Distributions

  • 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.

  • Topic 12

    Estimation II (2 weeks)

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

  • Topic 13

    Distribution Fitting

  • Topic 14

    Simple Linear Regression