IND 2149080 • Midterm + Final • Probability and Random Variables

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

Combinatorial Proof

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

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

Discrete Random Variables and Examples

Exam Like Question

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

Discrete Uniform Distribution Part 1

Discrete Uniform Distribution Part 2

Example 13

Example 14

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

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

Bayes' Rule 7

Bayes' Rule 8

Bayes' Rule 9

Discrete Random Variables 1

Discrete Random Variables 2

Discrete Random Variables 3

Discrete Random Variables 4

Discrete Random Variables 5

Discrete Random Variables 6

Discrete Random Variables 7

Discrete Random Variables 8

Discrete Random Variables 9

Moment Generating Function 1

Moment Generating Function 2

Moment Generating Function 3

Moment Generating Function 4

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Binomial Distribution 4

Binomial Distribution 5

Binomial Distribution 6

Poisson Distribution 1

Poisson Distribution 2

Poisson Distribution 3

Poisson distribution 4

Poisson Distribution 5

Poisson Approximation to Binomial 1

Poisson Approximation to Binomial 2

Hypergeometric Distribution 1

Hypergeometric Distribution 2

Hypergeometric Distribution 3

Hypergeometric Distribution 4

Negative Binomial Distribution 1

Negative Binomial - Geometric Distribution

Geometric Distribution 1

Geometric Distribution 2

Geometric Distribution 3

Discrete Uniform Distribution

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

Uniform Distribution

Example 1

Example 2

Exponential Distribution

Example 3

Example 4

Memoryless Property

Example 5

Normal Distribution

Standard Normal Distribution

Reading Z Table - Option 1

Reading Z Table - Option 2

Example 6

Continuous Random Variables and Examples

Exam Like Question

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

Covariance

Example 1 (Discrete)

Example 2 (Continuous)

Example 3 (Continuous)

Exam Like Question 1

Exam Like Question 2

Variance of Sums

Example 4

Correlation

Example 5

Exam Like Question 3

Exam Like Question 4

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

Uniform Distribution 1

Uniform Distribution 2

Uniform Distribution 3

Exponential Distribution 1

Exponential Distribution 2

Exponential Distribution 3

Exponential Distribution 4

Exponential Distribution 5

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3

Normal Distribution 4

Normal Distribution 5

Normal Distribution 6

Normal Distribution 7

Discrete Joint Probability 1

Discrete Joint Probability 2

Discrete Joint Probability 3

Discrete Joint Probability 4

Discrete Joint Probability 5

Discrete Joint Probability 6

Discrete Joint Distribution 7

Continuous Joint Probability 1

Continuous Joint Probability 2

Continuous Joint Probability 3

Continuous Joint Probability 4

Continuous Joint Probability 5

Continuous Joint Probability 6

Continuous Joint Probability 7

Continuous Joint Probability 8

Continuous Joint Probability 9

Continuous Joint Probability 10

Continuous Joint Probability 11

Covariance 1

Covariance 2

Covariance 3

Covariance 4

Covariance 5

Covariance 6

Covariance 7

Covariance 8

Covariance 9

Covariance 10

Covariance and Correlation Coefficient