IE 211 • Midterm • Probability Theory

Introduction

Frequency Distribution

Example 1

Relative Frequency Distribution

Example 2

Cumulative Frequency Distribution

Example 3

Frequency Histogram

Measures of Central Location

Example 4

Measures of Variability

Example 5

Example 6

Example 7

Skewness and Kurtosis

Stem and Leaf Diagram

Example 8

Example 9

Box and Whisker Plot

Example 10

Comparing Boxplots

Example 11

Example 12

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

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

Chebyshev's Theorem

Example 14

Descriptive Statistics 1

Descriptive Statistics 2

Descriptive Statistics 3

Descriptive Statistics 4

Descriptive Statistics 5

Descriptive Statistics 6

Counting 1

Counting 2

Counting 3

Counting 4

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Axioms of Probability 5

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

Bayes' Rule 1

Bayes' Rule 2

Bayes' Rule 3

Bayes' Rule 4

Bayes' Rule 5

Discrete Random Variable 1

Discrete Random Variable 2

Discrete Random Variable 3

Discrete Random Variable 4

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Discrete Joint Probability 1

Discrete Joint Probability 2

Discrete Joint Probability 3

Continuous Joint Probability 1

Continuous Joint Probability 2

Continuous Joint Probability 3

Mathematical Expectation 1 - Discrete R.V.

Mathematical Expectation 2 - Discrete R.V.

Mathematical Expectation 3 - Discrete R.V

Mathematical Expectation 4 - Discrete R.V.

Mathematical Expectation 5 - Discrete R.V.

Mathematical Expectation 6 - Continuous R.V.

Mathematical Expectation 7 - Continuous R.V.

Mathematical Expectation 8 - Discrete Joint

Mathematical Expectation 9 - Continuous Joint

Mathematical Expectation 10 - Continuous Joint

Mathematical Expectation 11 - Covariance

Mathematical Expectation 12 - Covariance

Mathematical Expectation 13 - Covariance

Chebyshev's Theorem 1

Chebyshev's Theorem 2