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