Probability Lecture Notes

 

 

Chapter I  

1.1 Introduction (Read)

1.2 The Basic Principle of Counting; (PDF)

1.3 Permutations; (PDF)

1.4 Combinations; (PDF)

1.5 Multinomial Coefficients (PDF)

 

 

Chapter II

2.1 Introduction

2.2 Sample Space and Events (PDF)

2.3 Axioms of Probability (PDF)

2.4 Some Simple Propositions (PDF)

2.5 Sample Spaces Having Equally Likely Outcomes (PDF)

 

 

 

Chapter III

3.1 Introduction

3.2 Conditional Probabilities (PDF)

3.3 Baye’s Formula & ODDS Notation (PDF)

3.4 Independent Events (PDF)

3.5 P(.|F) is a Probability (PDF)

 

 

Chapter IV

4.1 Random Variables (PDF)

4.2 Discrete Random Variables (PDF)

4.3 Expected Value (PDF)

4.4 Expectation of a Function of a Random Variable (PDF)

4.5 Variance (PDF)

4.6 Bernoulli and Binomial R.V. (PDF)

4.7 Poisson R.V. (PDF)

4.8.1 Geometric R.V. (PDF)

4.9 Expected Value of Sums of R.V.s (PDF)

4.10 Properties of the Cumulative Distribution Function

 

 

Chapter V

5.1 Introduction

5.2 Expectation and Variance of Continuous R.V.s

5.3 The uniform R.V.

5.4 Normal R.V.s

5.5 Exponential R.V.s

5.7 Distribution of a Function of a R.V.

 

 

Chapter VI

6.1 Joint Distribution Functions

6.2 Independent R.V.s

6.3 Sums of Independent R.V.s

6.4 Conditional Distributions: Discrete Case

6.5 Conditional Distributions: Continuous Case

 

 

Chapter VII

7.1 Introduction

7.2 Expectation of Sums of R.V.s

7.4 Covariance, Variance of Sums and Correlation

7.5 Conditional Expectation