MCB 1007 • Midterm I • Introduction to Probability Theory 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

Binomial Theorem

Example 1

Example 2

Example 3

Pascal Identity

Vandermonde's Identity

Example 1

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

Counting 1

Counting 2

Counting 3

Counting 4

Binomial Theorem

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Axioms of Probability 5

Axioms of Probability 6

Axioms of Probability 7

Axioms of Probability 8

Axioms of Probability 9

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) 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 Random Variable 1

Discrete Random Variable 2

Discrete Random Variable 3

Discrete Random Variable 4

Discrete Random Variable 5

Continuous Random Variable 1

Continuous Random Variable 2

Continuous Random Variable 3

Continuous Random Variable 4

Continuous Random Variable 5

Continuous Random Variable 6

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

Expected Value and Variance for Continuous Joint RV

Multivariate Distribution - Discrete 1

Multivariate Distribution - Discrete 2

Multivariate Distribution - Discrete 3

Multivariate Distribution - Discrete 4

Multivariate Distribution - Continuous 1

Multivariate Distribution - Continuous 2

Multivariate Distribution - Continuous 3

Multivariate Distribution - Continuous 4

Expected Value of a Discrete Random Variable

Expected Value of a Discrete Random Variable

Variance of a Discrete Random Variable

Expected Value of a Discrete Random Variable

Expected Value and Variance of a Continuous Random Variable

Expected Value of a Continuous Random Variable

Expected Value of a Continuous Random Variable

Expected Value of a Continuous Random Variable

Variance of a Continuous Random Variable