MAT 271E • Midterm • Probability for Computer Engineering

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example 1

Identical Objects Example 2

Identical Objects Example 3

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

Random Variables

Probability Mass Function

Example 1

Example 2

Cumulative Distribution Function

Example 3

Expected Value

Example 4

Example 5

Variance

Example 6

Example 7

Bernoulli Distribution Part 1

Bernoulli Distribution Part 2

Example 1

Example 2

Binomial Distribution Part 1

Binomial Distribution Part 2

Example 3

Example 4

Poisson Distribution Part 1

Poisson Distribution Part 2

Example 5

Example 6

Poisson Approximation to Binomial Distribution

Example 7

Hypergeometric Distribution

Example 1

Geometric Distribution Part 1

Geometric Distribution Part 2

Example 2

Example 3

Negative Binomial Distribution Part 1

Negative Binomial Distribution Part 2

Example 4

Example 5

Combinatorial Analysis 1

Combinatorial Analysis 2

Combinatorial Analysis 3

Combinatorial Analysis 4

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Axioms of Probability 5

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

Bayes' Rule 1

Bayes' Rule 2

Bayes' Rule 3

Bayes' Rule 4

Bayes' Rule 5

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

Discrete Random Variable 8

Discrete Random Variable 9

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Poisson distribution 1

Poisson distribution 2

Poisson Distribution 3

Hypergeometric Distribution 1

Hypergeometric Distribution 2

Negative Binomial Distribution

Negative Binomial - Geometric Distribution

Geometric Distribution 1

Geometric Distribution 2