IE 2531 • Final • Probability for Engineering

Probability Density Function - PDF

Example 1

Cumulative Distribution Function - CDF

Example 2

Expected Value

Expected Value - Example 1

Expected Value - Example 2

Variance

Variance - Example 1

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

Normal Approximation to Binomial Distribution

Example 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

Covariance

Example 1 (Discrete)

Example 2 (Continuous)

Example 3 (Continuous)

Variance of Sums

Example 4

Correlation Coefficient

Example 5

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Random Variables 5

Uniform Distribution 1

Uniform Distribution 2

Uniform Distribution 3

Exponential Distribution 1

Exponential Distribution 2

Exponential Distribution 3

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3

Normal Distribution 4

Normal Distribution 5

Normal Distribution 6

Normal Distribution 7

Discrete Joint Probability 1

Discrete Joint Probability 2

Discrete Joint Probability 3

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

Covariance 1

Covariance 2

Covariance 3

Covariance 4

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6