MATH 230 • Midterm I • Introduction to Probability Theory

Sample Space and Events

Probability

Axioms of Probability

Some Rules

Coin Example

Dice Example

Card Example 1

Card Example 2

Ball Example

Set Example

Birthday Example

Conditioning Events

Total Probability Rule

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Bayes' Rule

Bayes' Rule Example 1

Bayes' Rule Example 2

Independence

Independence Example 1

Independence Example 2

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Conditional Probability and Independence 1

Conditional Probability and Independence 2

Conditional Probability and Independence 3

Conditional Probability and Independence 4

Conditional Probability and Independence 5

Conditional Probability and Independence 6

Conditional Probability and Independence 7

Conditional Probability and Independence 8

Conditional Probability and Independence 9

Bayes' Rule 1

Bayes' Rule 2

Bayes' Rule 3

Bayes' Rule 4

Bayes' Rule 5

Bayes' Rule 6

Bayes' Rule 7

Bayes' Rule 8

Bayes' Rule 9

Random Variables

Probability Mass Function (PMF) for Discrete RV

PMF Example 1

PMF Example 2

Cumulative Distribution Function for Discrete RV

CDF Example

Probability Density Function (PDF) for Continuous RV

PDF Example

Cumulative Distribution Function (CDF) for Continuous RV

CDF Example

Discrete Random Variable 1

Discrete Random Variable 2

Discrete Random Variable 3

Discrete Random Variable 4

Discrete Random Variable 5

Discrete Random Variable 6

Discrete Random Variable 7

Continuous Random Variable 1

Continuous Random Variable 2

Continuous Random Variable 3

Continuous Random Variable 4

Continuous Random Variable 5

Continuous Random Variable 6

Continuous Random Variable 7