MATH 203 • Midterm I • Introduction to Probability

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example 1

Combination

n choose r

Committee Example

Ball Example

Sample Space and Events

Probability

Axioms of Probability

Some Rules

Coin Example

Dice Example

Card Example 1

Card Example 2

Ball Example

Set 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

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

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

Introduction

Formulas

Properties

Example 1

Example 2

Example 3

Example 4

Axioms of Probability 1 (Spring 2022)

Axioms of Probability 2 (Fall 2022)

Axioms of Probability 3 (Spring 2022)

Conditional Probability (Spring 2023)

Conditional Probability and Independence 1 (Fall 2022)

Conditional Probability and Independence 2 (Spring 2022)

Bayes' Rule 1 (Fall 2022)

Bayes' Rule 2 (Spring 2022)

Bayes' Rule 3 (Spring 2023)

Discrete Random Variables 1 (Fall 2022)

Discrete Random Variables 2 (Spring 2023)

Poisson Distribution 1 (Spring 2022)

Poisson Distribution 2 (Fall 2022)

Binomial Distribution (Fall 2022)

Poisson Approximation to Binomial (Spring 2023)

Moment Generating Function 1 (Fall 2022)

Moment Generating Function 2 (Spring 2022)

Moment Generating Function 3 (Spring 2023)

Bayes' Rule

Discrete Random Variables 1

Discrete Random Variables 2

Binomial Distribution

Continuous Random Variables 1 (Midterm I'de yok!)

Continuous Random Variables 2 (Midterm I'de yok!)

Counting 1

Counting 2

Bayes' Rule 1

Bayes' Rule 2

Discrete Random Variable 1

Discrete Random Variable 2

Binomial Distribution 1

Binomial Distribution 2

Poisson Distribution

Negative Binomial & Geometric Distribution

Negative Binomial Distribution