IE 211 • Final • Probability Theory

Expected Value for Discrete RV

Example 1

Example 2

Variance for Discrete RV

Example 3

Example 4

Expected Value for Continuous RV

Example 5

Example 6

Variance for Continuous RV

Example 7

Expected Value for Discrete Joint RV

Variance for Discrete Joint RV

Example 8

Conditional Expectation for Discrete Joint RV

Example 9

Example 10

Expected Value and Variance for Continuous Joint RV

Conditional Expectation for Continuous Joint RV

Example 11

Example 12

Example 13

Covariance

Correlation

Discrete Uniform Distribution Part 1

Discrete Uniform Distribution Part 2

Bernoulli Distribution Part 1

Bernoulli Distribution Part 2

Binomial Distribution Part 1

Binomial Distribution Part 2

Poisson Distribution Part 1

Poisson Distribution Part 2

Poisson Approximation to Binomial Distribution

Geometric Distribution Part 1

Geometric Distribution Part 2

Hypergeometric Distribution

Negative Binomial Distribution Part 1

Negative Binomial Distribution Part 2

Uniform Distribution

Example 1

Example 2

Exponential Distribution

Example 3

Example 4

Memoryless Property

Example 5

Normal Distribution

Standard Normal Distribution

Reading Z Table - Option 1

Reading Z Table - Option 2

Example 6

Gamma Distribution

Example 7

Relation of Gamma Distribution with Others

Weibull Distribution

Continuous One Variable Case

Example 1

Example 2

Continuous Multivariable Case

Example 3

Introduction

Formulas

Properties

Example 1

Example 2

Example 3

Example 4

Example 5

Mathematical Expectation 1 - Discrete R.V.

Mathematical Expectation 2 - Discrete R.V.

Mathematical Expectation 3 - Discrete R.V

Mathematical Expectation 4 - Discrete R.V.

Mathematical Expectation 5 - Discrete R.V.

Mathematical Expectation 6 - Continuous R.V.

Mathematical Expectation 7 - Continuous R.V.

Mathematical Expectation 8 - Discrete Joint

Mathematical Expectation 9 - Continuous Joint

Mathematical Expectation 10 - Continuous Joint

Mathematical Expectation 11 - Covariance

Mathematical Expectation 12 - Covariance

Mathematical Expectation 13 - Covariance

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Poisson distribution 1

Poisson distribution 2

Poisson Distribution 3

Hypergeometric Distribution 1

Hypergeometric Distribution 2

Negative Binomial Distribution

Negative Binomial - Geometric Distribution

Geometric Distribution 1

Geometric Distribution 2

Uniform Distribution - Continuous

Exponential Distribution 1

Exponential Distribution 2

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3

Normal Distribution 4

Normal Distribution 5

Normal Distribution 6

Moment Generating Functions 1

Moment Generating Functions 2