MATH 215 • Midterm I • Probability and Random Variables

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example 1

Identical Objects Example 2

Combination

n choose r

Committee Example 1

Committee Example 2

Ball Example 1

Ball Example 2

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 1

Conditional Probability 2

Conditional Probability 3

Conditional Probability 4

Independence 1

Independence 2

Conditional Probability and Independence

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 Example 1

PMF Example 2

Cumulative Distribution Function

CDF Example 1

Expected Value

Expected Value Example 1

Expected Value Example 2

Variance

Variance Example 1

Variance Example 2

Discrete Uniform Distribution Part 1

Discrete Uniform Distribution Part 2

Example 1

Example 2

Bernoulli Distribution Part 1

Bernoulli Distribution Part 2

Example 3

Example 4

Binomial Distribution Part 1

Binomial Distribution Part 2

Example 5

Example 6

Geometric Distribution Part 1

Geometric Distribution Part 2

Example 1

Example 2

Hypergeometric Distribution

Example 3

Negative Binomial Distribution Part 1

Negative Binomial Distribution Part 2

Example 4

Example 5

Poisson Distribution Part 1

Poisson Distribution Part 2

Example 7

Example 8

Poisson Approximation to Binomial Distribution

Example 9

Discrete Random Variables 1

Discrete Random Variables 2

Discrete Random Variables 3

Discrete Random Variables 4

Discrete Random Variables 5

Discrete Random Variables 6

Discrete Random Variables 7

Discrete Random Variables 8

Discrete Random Variables 9

Discrete Random Variables 10

Discrete Random Variables 11

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Binomial Distribution 4

Poisson distribution 1

Poisson Distribution 2

Poisson Distribution 3

Poisson distribution 4

Hypergeometric Distribution 1

Hypergeometric Distribution 2

Hypergeometric Distribution 3

Hypergeometric Distribution 4

Discrete Uniform Distribution

Negative Binomial Distribution 1

Negative Binomial - Geometric Distribution

Geometric Distribution 1

Geometric Distribution 2

Geometric Distribution 3

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