Elements of Probability and Statistics
ELEMENTS OF PROBABILITY AND STATISTICS
Instructor: Ceylan YOZGATLIGİL
Added: 15 March 2010
- Topic 1Introduction
Probability Axioms, Combinatorics
- Topic 2Conditional Probability and Bayes Theorem
- Topic 3Random 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 6Mgf and Distributions (2 weeks)
Moment generating functions, Statistical Distributions: Discrete distributions and their properties, Continuous distributions and their properties.
- Topic 8Limiting Distributions & Sampling Distributions
- Topic 9Point 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 12Estimation II (2 weeks)
Testing hypotheses: concepts of hypothesis testing, Neyman-Pearson lemma, Likelihood ratio test, Confidence intervals
- Topic 13
- Topic 14Simple Linear Regression