MATH 227 • Final • Probability and Statistics for Engineering I

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

Discrete Joint Probability 1

Discrete Joint Probability 2

Discrete Joint Probability 3

Discrete Joint Probability 4

Discrete Joint Probability 5

Discrete Joint Probability 6

Discrete Joint Distribution 7

Introduction

Marginal PDF and CDF

Expected Value and Variance

Conditional PDF and CDF

Conditional Expectation

Example 1

Example 2

Example 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

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

Covariance 1

Covariance 2

Covariance 3

Covariance 4

Covariance 5

Covariance 6

Covariance 7

Covariance 8

Covariance 9

Covariance 10

Covariance and Correlation Coefficient

Axioms of Probability

Conditional Probability

Conditional Probability and Independence

Bayes' Rule

Discrete Random Variables 1

Discrete Random Variables 2

Moment Generating Function - Discrete

Binomial Distribution

Poisson Distribution

Negative Binomial - Geometric Distribution

Continuous Random Variables 1

Continuous Random Variables 2

Moment Generating Function - Continuous

Exponential Distribution

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3