MAT 3027 • Midterm • 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

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

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

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

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

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

Discrete Random Variables 1

Discrete Random Variables 2

Discrete Random Variables 3

Discrete Random Variables 4

Discrete Random Variables 5

Discrete Random Variable 6

Discrete Random Variable 7

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Random Variables 5

Continuous Random Variables 6

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 8

Geometric Distribution Part 1

Geometric Distribution Part 2

Example 9

Example 10

Negative Binomial Distribution Part 1

Negative Binomial Distribution Part 2

Example 11

Example 12

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

Gamma Distribution

Example 8

Relation of Gamma Distribution with Others

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

Negative Binomial Distribution 1

Negative Binomial - Geometric Distribution

Geometric Distribution 1

Geometric Distribution 2

Geometric Distribution 3

Continuous Uniform Distribution 1

Continuous Uniform Distribution 2

Continuous Uniform Distribution 3

Exponential Distribution 1

Exponential Distribution 2

Exponential Distribution 3

Exponential Distribution 4

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3

Normal Distribution 4

Normal Distribution 5

Normal Distribution 6

Normal Distribution 7