MATH 230 (Fall 23) • Probability and Statistics for Engineering • Midterm

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Counting Techniques

Combination vs Permutation

Combination

Permutation

Conditional Probability I

Conditional Probability II

Total Probability Rule

Bayes' Rule

Independence I

Independence II

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

Bayes' Rule 1

Bayes' Rule 2

Bayes' Rule 3

Bayes' Rule 4

Bayes' Rule 5

Probability Mass Functions

Expected Value

PMF Tables

Cumulative Distribution Function

Variance

Variance Arithmetic

Moment Generating Functions and Examples

Example 1

Chebyshev's Inequality

Example 2

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

Discrete Random Variables 1

Discrete Random Variables 2

Discrete Random Variables 3

Discrete Random Variables 4

Moment Generating Function 1

Moment Generating Function 2

Moment Generating Function 3

Moment Generating Function 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

What is continuous anyway?

Expected Value and Variance

Cumulative Distribution Function (CDF)

Finding f(x) Given F(x)

Example 1

Example 2

Moment Generating Functions and Examples

Example 3

Normal Distribution

Standard Normal Distribution

Reading Z Table

Example 1

Example 2

Normal Approximation to Binomial Distribution

Example 3

Exponential Distribution

Example 4

Example 5

Memoryless Property

Example 6

Example 7

Gamma Distribution

Example 8

Relation of Gamma Distribution with Others

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