MATH 281 • Probability • Midterm

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

Bayes' Rule

Bayes' Rule Example 1

Bayes' Rule Example 2

Independence

Independence Example 1

Independence Example 2

Counting 1 - Product Rule

Counting 2 - Product Rule

Counting 3 - Product Rule

Counting 4 - Product Rule

Counting 5 - Permutations

Counting 6 - Permutations

Counting 7 - Permutations

Counting 8 - Permutations

Counting 9 - Permutations

Counting 10 - Permutations

Counting 11 - Circular Permutation

Counting 12 - Repeated Permutation

Counting 13 - Combinations

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

Bayes' Rule 1

Bayes' Rule 2

Bayes' Rule 3

Bayes' Rule 4

Bayes' Rule 5

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 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

Geometric Distribution Part 1

Geometric Distribution Part 2

Example 8

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

Poisson Distribution 1

Poisson Distribution 2

Poisson Distribution 3

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Binomial Distribution 4

Poisson Approximation to Binomial 1

Poisson Approximation to Binomial 2

Geometric Distribution 1

Geometric Distribution 2

Geometric Distribution 3

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

Uniform Distribution

Example 1

Example 2

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Random Variables 5

Continuous Random Variables 6

Uniform Distribution 1

Uniform Distribution 2

Uniform Distribution 3