MAT 3027 • Final • Probability and Random Variables

Probability Mass Function

PMF Example

Marginal PMF and CDF

Expected Value

Variance

Expected Value and Variance Example

Conditional PMF and CDF

Conditional Expectation

End of Topic Example - Part I

End of Topic Example - Part II

Introduction

Marginal PDF and CDF

Expected Value and Variance

Conditional PDF and CDF

Conditional Expectation

Example 1

Example 2

Example 3

Discrete Joint Probability 1

Discrete Joint Probability 2

Discrete Joint Probability 3

Discrete Joint Probability 4

Discrete Joint Probability 5

Continuous Joint Probability 1

Continuous Joint Probability 2

Continuous Joint Probability 3

Continuous Joint Probability 4

Continuous Joint Probability 5

Continuous Joint Probability 6

Continuous Joint Probability 7

Continuous Joint Probability 8

Continuous Joint Probability 9

Continuous Joint Probability 10

Continuous Joint Probability 11

Covariance

Example 1 (Discrete)

Example 2 (Continuous)

Example 3 (Continuous)

Exam Like Question 1

Exam Like Question 2

Variance of Sums

Example 4

Correlation

Example 5

Exam Like Question 3

Exam Like Question 4

Distribution Function Techniques

Example 1

Example 2

Example 3

Example 4

Example 5

Joint Statistics 1

Joint Statistics 2

Joint Statistics 3

Joint Statistics 4

Joint Statistics 5

Joint Statistics 6

Joint Statistics 7

Joint Statistics 8

Joint Statistics 9

Distribution Function Technique 1

Distribution Function Technique 2

Distribution Function Technique 3

Distribution Function Technique 4

Distribution Function Technique 5

Distribution Function Technique 6

Distribution Function Technique 7

Sample Mean

Sample Variance

Introduction

Example 1

Example 2

Example 3

Example 4

Example 5

Normal Approximation to Binomial Distribution

Normal Approximation to Poisson Distribution

Central Limit Theorem 1

Central Limit Theorem 2

Central Limit Theorem 3

Central Limit Theorem 4

Central Limit Theorem 5

Normal Approximation to Binomial 1

Normal Approximation to Binomial 2