CENG 235 • Midterm • Introduction To Probability and Statistics

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

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

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

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

Bayes' Rule 1

Bayes' Rule 2

Bayes' Rule 3

Bayes' Rule 4

Bayes' Rule 5

Bayes' Rule 6

Bayes' Rule 7

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

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

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

Probability Mass Function

PMF Example

Marginal PMF and CDF

Expected Value

Variance

Expected Value and Variance Example

Conditional PMF and CDF

Conditional Expectation

End of Topic Example - Part I

End of Topic Example - Part II

Introduction

Marginal PDF and CDF

Expected Value and Variance

Conditional PDF and CDF

Conditional Expectation

Example 1

Example 2

Example 3

Discrete Joint Probability 1

Discrete Joint Probability 2

Discrete Joint Probability 3 - Expected Value

Discrete Joint Probability 4 - Expected Value

Continuous Joint Probability 1

Continuous Joint Probability 2

Continuous Joint Probability 3

Continuous Joint Probability 4

Continuous Joint Probability 5 - Expected Value

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

Normal Approximation to Binomial Distribution

Example 9

Geometric Distribution Part 1

Geometric Distribution Part 2

Example 10

Example 11

Negative Binomial Distribution Part 1

Negative Binomial Distribution Part 2

Example 12

Example 13

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Multinomial Distribution 1

Multinomial Distribution 2

Poisson distribution 1

Poisson Distribution 2

Poisson Distribution 3

Poisson distribution 4

Hypergeometric Distribution 1

Hypergeometric Distribution 2

Hypergeometric Distribution 3

Hypergeometric Distribution 4

Hypergeometric Distribution 5

Negative Binomial Distribution 1

Negative Binomial - Geometric Distribution