MATH 230 • Probability and Statistics for Engineering • 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

Counting 1 - Product Rule

Counting 2 - Product Rule

Counting 3 - Permutations

Counting 4 - Permutations

Counting 5 - Permutations

Counting 6 - Permutations

Counting 7 - Circular Permutation

Counting 8 - Repeated Permutation

Counting 9 - Combinations

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

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Conditioning Events

Total Probability Rule

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Independence

Independence Example 1

Independence Example 2

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

Conditional Probability and Independence 6

Conditional Probability and Independence 7

Conditional Probability and Independence 8

Conditional Probability and Independence 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 Random Variable 1

Discrete Random Variable 2

Discrete Random Variable 3

Discrete Random Variable 4

Discrete Random Variable 5

Discrete Random Variable 6 - Expected Value

Discrete Random Variable 7 - Expected Value

Discrete Random Variable 8 - Variance

Discrete Random Variable 9 - Expected Value

Bernoulli Distribution - 1

Bernoulli Distribution - 2

Example 1

Binomial Distribution - 1

Binomial Distribution - 2

Example 2

Example 3

Negative Binomial Distribution - 1

Negative Binomial Distribution - 2

Example 4

Hypergeometric Distribution

Example 5

Poisson Distribution - 1

Poisson Distribution - 2

Example 6

Example 7

Poisson Approximation to Binomial Distribution

Example 8

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Poisson distribution 1

Poisson Distribution 2

Poisson Distribution 3

Poisson distribution 4

Hypergeometric Distribution 1

Hypergeometric Distribution 2

Hypergeometric Distribution 3

Discrete Uniform Distribution

Negative Binomial Distribution 1

Negative Binomial - Geometric Distribution

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 Variable 1

Continuous Random Variable 2

Continuous Random Variable 3

Continuous Random Variable 4

Continuous Random Variable 5 - Expected Value

Continuous Random Variable 6 - Expected Value

Continuous Random Variable 7 - Variance

Continous Random Variable 8 - Expected Value

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 8

Relation of Gamma Distribution with Others

Continuous Uniform Distribution

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3

Normal Distribution 4

Normal Distribution 5

Normal Distribution 6

Normal Distribution 7

Exponential Distribution 1

Exponential Distribution 2

Exponential Distribution 3

Counting

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Conditional Probability 1

Conditional Probability 2

Conditional Probability 3

Conditional Probability 4

Independence 1

Independence 2

Independence 3

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

Poisson Distribution 1

Poisson Distribution 2

Poisson Distribution 3

Poisson Approximation to Binomial Distribution 1

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Exponential Distribution 1

Exponential Distribution 2

Exponential Distribution 3

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3