## Konu özeti

• ### Genel

ELEMENTS OF PROBABILITY AND STATISTICS

 Instructor: Ceylan YOZGATLIGİL Added: 15 March 2010
• ### Konu 1

Introduction

Probability Axioms, Combinatorics

• ### Konu 2

Conditional Probability and Bayes Theorem

• ### Konu 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.

• ### Konu 6

Mgf and Distributions (2 weeks)

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

• ### Konu 8

Limiting Distributions & Sampling Distributions

• ### Konu 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.

• ### Konu 12

Estimation II (2 weeks)

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

• ### Konu 13

Distribution Fitting

• ### Konu 14

Simple Linear Regression