CE 217 • Midterm • Probability and Statistics in Civil Engineering

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

Example 5

Example 6

Bayes' Rule

Bayes' Rule Example 1

Bayes' Rule Example 2

Independence

Independence Example 1

Independence Example 2

Probability 1

Probability 2

Probability 3

Probability 4

Conditional Probability 1

Conditional Probability 2

Conditional Probability 3

Conditional Probability 4

Independence 1

Independence 2

Conditional Probability and Independence

Bayes' Rule 1

Bayes' Rule 2

Bayes' Rule 3

Bayes' Rule 4

Bayes' Rule 5

Bayes' Rule 6

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

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

Introduction

Formulas

Properties

Example 1

Example 2

Example 3

Example 4

Example 5

Discrete Random Variables 1

Discrete Random Variables 2

Discrete Random Variables 3

Discrete Random Variables 4

Discrete Random Variables 5

Discrete Random Variables 6

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Random Variables 5

Continuous Random Variables 6

Moment Generating Function 1

Moment Generating Function 2

Moment Generating Function 3

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

Exponential Distribution

Example 1

Example 2

Memoryless Property

Example 3

Normal Distribution

Standard Normal Distribution

Reading Z Table - Option 1

Reading Z Table - Option 2

Example 4

Gamma Distribution

Example 5

Relation of Gamma Distribution with Others

Sample Mean

Sample Variance

Example 1

Central Limit Theorem

Example 2

Example 3

Example 4

Example 5

Example 6

Normal Approximation to Binomial Distribution

Normal Approximation to Poisson Distribution

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Poisson distribution 1

Poisson Distribution 2

Poisson Distribution 3

Hypergeometric Distribution 1

Hypergeometric Distribution 2

Negative Binomial Distribution 1

Negative Binomial - Geometric Distribution

Geometric Distribution 1

Geometric Distribution 2

Exponential Distribution 1

Exponential Distribution 2

Exponential Distribution 3

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3

Normal Distribution 4

Normal Distribution 5

Normal Distribution 6

Normal Distribution 7

Central Limit Theorem 1

Central Limit Theorem 2

Central Limit Theorem 3

Central Limit Theorem 4

Central Limit Theorem 5

Normal Approximation to Binomial 1