### General

** ELEMENTS OF PROBABILITY AND STATISTICS**

Instructor: Ceylan YOZGATLIGİL Added: 15 March 2010 |

### 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 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