MATH 250 • Introduction to Probability • Midterm

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

Ball Example 1

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

Bayes' Rule

Bayes' Rule Example 1

Bayes' Rule Example 2

Independence

Independence Example 1

Independence Example 2

Counting 1

Axioms of Probability 1

Axioms of Probability 2

Conditional Probability 1

Conditional Probability 2

Conditional Probability 3

Conditional Probability 4

Conditional Probability 5

Conditional Probability 6

Conditional Probability 7

Conditional Probability 8

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

Bernoulli Distribution - 1

Bernoulli Distribution - 2

Example 1

Example 2

Binomial Distribution - 1

Binomial Distribution - 2

Example 3

Example 4

Negative Binomial Distribution - 1

Negative Binomial Distribution - 2

Example 5

Example 6

Geometric Distribution - 1

Geometric Distribution - 2

Example 1

Example 2

Hypergeometric Distribution

Example 3

Poisson Distribution - 1

Poisson Distribution - 2

Example 4

Example 5

Poisson Approximation to Binomial Distribution

Example 6

Discrete Random Variables 1

Discrete Random Variables 2

Discrete Random Variables 3

Discrete Random Variables 4

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Binomial Distribution 4

Binomial Distribution 5

Binomial Distribution 6

Binomial Distribution 7

Binomial Distribution 8

Binomial Distribution 9

Binomial Distribution 10

Negative Binomial Distribution 1

Negative Binomial Distribution 2

Negative Binomial Distribution 3

Negative Binomial Distribution 4

Negative Binomial Distribution 5

Negative Binomial Distribution 6

Geometric Distribution 1

Geometric Distribution 2

Geometric Distribution 3

Geometric Distribution 4

Geometric Distribution 5

Geometric Distribution 6

Geometric Distribution 7

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

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Random Variables 5

Continuous Random Variables 6

Continuous Random Variable 7

Continuous Random Variable 8

Continuous Random Variable 9

Continuous Random Variable 10

Continuous Random Variable 11

Continuous Random Variable 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

Gamma Distribution

Example 7

Relation of Gamma Distribution with Others

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9