MATH 210 • Midterm • Probability and Statistics

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Combination

n choose r

Sample Space and Events

Probability

Axioms of Probability

Some Rules

Coin Example

Dice Example

Card Example 1

Card Example 2

Ball Example

Set Example

Conditional Probability

Total Probability Rule

Example 1

Example 2

Example 3

Bayes' Rule

Example 4

Example 5

Independence

Example 6

Random Variables

Probability Mass Function (PMF) for Discrete RV

PMF Example 1

PMF Example 2

Cumulative Distribution Function for Discrete RV

CDF Example

Probability Density Function (PDF) for Continuous RV

PDF Example

Cumulative Distribution Function (CDF) for Continuous RV

CDF Example

Discrete Joint Random Variables

Discrete Joint RV Example

Marginal PMF and CDF for Discrete Joint RV

Conditional PMF and CDF for Discrete Joint RV

Continuous Joint Random Variables

Marginal PDF and CDF for Continuous Joint RV

Conditional PDF and CDF for Continuous Joint RV

Expected Value for Discrete RV

Example 1

Example 2

Variance for Discrete RV

Example 3

Example 4

Expected Value for Continuous RV

Example 5

Example 6

Variance for Continuous RV

Example 7

Expected Value for Discrete Joint RV

Variance for Discrete Joint RV

Example 8

Conditional Expectation for Discrete Joint RV

Example 9

Example 10

Expected Value and Variance for Continuous Joint RV

Conditional Expectation for Continuous Joint RV

Example 11

Example 12

Example 13

Covariance

Correlation

Discrete Uniform Distribution Part 1

Discrete Uniform Distribution Part 2

Bernoulli Distribution Part 1

Bernoulli Distribution Part 2

Binomial Distribution Part 1

Binomial Distribution Part 2

Poisson Distribution Part 1

Poisson Distribution Part 2

Poisson Approximation to Binomial Distribution

Geometric Distribution Part 1

Geometric Distribution Part 2

Hypergeometric Distribution

Negative Binomial Distribution Part 1

Negative Binomial Distribution Part 2

Uniform Distribution

Exponential Distribution

Example

Memoryless Property

Normal Distribution

Standard Normal Distribution

Reading Z Table - Option 1

Reading Z Table - Option 2

Gamma Distribution

Relation of Gamma Distribution with Others

Weibull Distribution

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22