MATH 215 • Tüm Sınavlar • 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

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 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

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 Uniform Distribution Part 1

Discrete Uniform Distribution Part 2

Example 1

Example 2

Bernoulli Distribution Part 1

Bernoulli Distribution Part 2

Example 3

Example 4

Binomial Distribution Part 1

Binomial Distribution Part 2

Example 5

Example 6

Geometric Distribution Part 1

Geometric Distribution Part 2

Example 1

Example 2

Hypergeometric Distribution

Example 3

Negative Binomial Distribution Part 1

Negative Binomial Distribution Part 2

Example 4

Example 5

Poisson Distribution Part 1

Poisson Distribution Part 2

Example 7

Example 8

Poisson Approximation to Binomial Distribution

Example 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

Discrete Random Variables 10

Discrete Random Variables 11

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 3

Binomial Distribution 4

Poisson distribution 1

Poisson Distribution 2

Poisson Distribution 3

Poisson distribution 4

Hypergeometric Distribution 1

Hypergeometric Distribution 2

Hypergeometric Distribution 3

Hypergeometric Distribution 4

Discrete Uniform Distribution

Negative Binomial Distribution 1

Negative Binomial - Geometric Distribution

Geometric Distribution 1

Geometric Distribution 2

Geometric Distribution 3

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35

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 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Random Variables 5

Continuous Random Variables 6

Uniform Distribution 1

Uniform Distribution 2

Uniform Distribution 3

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

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

Distribution Function Techniques

Example 1

Example 2

Example 3

Example 4

Discrete Joint Probability 1

Discrete Joint Probability 2

Discrete Joint Probability 3

Discrete Joint Probability 4

Discrete Joint Probability 5

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

Functions of Random Variables 1

Functions of Random Variables 2

Functions of Random Variables 3

Functions of Random Variables 4

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Conditional Probability 1

Discrete Random Variables 1

Discrete Random Variables 2

Poisson Approximation to Binomial Distribution 1

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Random Variables 5

Exponential Distribution 1

Normal Distribution 1

Normal Distribution 2

Discrete Joint Distribution 1

Discrete Joint Distribution 2

Discrete Joint Distribution 3

Discrete Joint Distribution 4

Discrete Joint Distribution 5

Continuous Joint Distribution 1

Continuous Joint Distribution 2

Continuous Joint Distribution 3

Covariance

Example 1

Example 2

Example 3

Exam Like Question 1

Exam Like Question 2

Variance of Sums

Example 4

Correlation

Example 5

Exam Like Question 3

Exam Like Question 4

Covariance and Correlation 1

Covariance and Correlation 2

Covariance and Correlation 3

Covariance and Correlation 4

Covariance and Correlation 5

Covariance and Correlation 6

Covariance and Correlation 7

Covariance and Correlation 8

Covariance and Correlation 9

Sample Mean

Sample Variance

Example 1

Central Limit Theorem

Example 1

Example 2

Example 3

Example 4

Example 5

Normal Approximation to Binomial Distribution

Normal Approximation to Poisson Distribution

Central Limit Theorem 1

Central Limit Theorem 2

Central Limit Theorem 3

Normal Approximation to Binomial 1

Normal Approximation to Binomial 2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11