Probability and Statistics

Week 1: Sets, Classes, Collections

Sequence of Sets

Ring, Field (Algebra)

Sigma-Ring, Sigma-Field, Monotone Class

Random Experiment, Events

Definitions of Probability

Properties of Probability Function-I

Properties of Probability Function-II

Week 2: Conditional Probability

Independence of Events

Problems in Probability-I

Problems in Probability-II

Random Variables

Probability Distribution of a Random Variable-I

Week 3: Probability Distribution of a Random Variable-II

Moments

Characteristics of Distributions-I

Characteristics of Distributions-II

Special Discrete Distributions-I

Special Discrete Distributions-II

Special Discrete Distributions-III

Week 4: Poisson Process-I

Poisson Process-II

Special Continuous Distributions-I

Special Continuous Distributions-II

Special Continuous Distributions-III

Special Continuous Distributions-IV

Special Continuous Distributions-V

Week 5: Normal Distribution

Problems on Normal Distribution

Problems on Special Distributions-I

Problems on Special Distributions-II

Function of a Random Variable-I

Function of a Random Variable-II

Week 6: Joint Distributions-I

Joint Distributions-II

Independence, Product Moments

Linearity Property of Correlation and Examples

Bivariate Normal Distribution-I

Bivariate Normal Distribution-II

Week 7: Additive Properties of Distributions-I

Additive Properties of Distributions-II

Transformation of Random Variables

Distribution of Order Statistics

Basic Concepts

Chi-Square Distribution

Week 8: Chi-Square Distribution 
(Cont…), t-Distribution

F-Distribution

Descriptive Statistics – I

Descriptive Statistics - II

Descriptive Statistics – III

Descriptive Statistics – IV

Week 9: Introduction to Estimation

Unbiased and Consistent Estimators

LSE, MME

Examples on MME, MLE

Examples on MLE-I

Examples on MLE-II, MSE

Week 10: UMVUE, Sufficiency, Completeness

Rao-Blackwell Theorem and its Applications

Confidence Intervals-I

Confidence Intervals- II

Confidence Intervals- III

Confidence Intervals- IV

Week 11: Basic Definitions

Two Types of Errors

Neyman-Pearson Fundamental Lemma

Applications of N-P Lemma-I

Applications of N-P Lemma-II

Week 12: Testing for Normal Mean

Testing for Normal Variance

Large Sample Test for Variance and Two Sample Problem

Paired t-Test

Examples

Week 13: Testing Equality of Proportions

Chi-Square Test for Goodness Fit -I

Chi-Square Test for Goodness Fit –II

Testing for Independence in  Contingency Table –I

Testing for Independence in  Contingency Table-II