END 252E • Midterm II + Final • Theory of Probability

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

Uniform Distribution 1

Uniform Distribution 2

Uniform Distribution 3

Exponential Distribution 1

Exponential Distribution 2

Exponential Distribution 3

Exponential Distribution 4

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3

Normal Distribution 4

Normal Distribution 5

Normal Distribution 6

Normal Distribution 7

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

Example 2

Example 3

Exam Like Question 1

Exam Like Question 2

Variance of Sums

Example 4

Correlation

Example 5

Exam Like Question 3

Exam Like Question 4

Introduction

Formulas

Properties

Example 1

Example 2

Example 3

Example 4

Example 5

Chebyshev's Inequality

Example 1

Sample Mean

Sample Variance

Example 2

Central Limit Theorem

Example 3

Example 4

Example 5

Example 6

Example 7

Normal Approximation to Binomial Distribution

Normal Approximation to Poisson Distribution

Covariance and Correlation 1

Covariance and Correlation 2

Covariance and Correlation 3

Covariance and Correlation 4

Covariance and Correlation 5

Covariance and Correlation 6

Covariance and Correlation 7

Covariance and Correlation 8

Covariance and Correlation 9

Chebyshev's Theorem 1

Chebyshev's Theorem 2

Central Limit Theorem 1

Central Limit Theorem 2

Central Limit Theorem 3

Central Limit Theorem 4

Central Limit Theorem 5

Central Limit Theorem 6

Central Limit Theorem 7

Normal Approximation to Binomial 1

Normal Approximation to Binomial 2

Moment Generating Function 1

Moment Generating Function 2

Moment Generating Function 3

Moment Generating Function 4