ENGR 200 • Final • Probability and Random Variables For Engineers

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

Introduction

Marginal PDF and CDF

Expected Value and Variance

Conditional PDF and CDF

Conditional Expectation

Example 1

Example 2

Example 3

Normal Distribution

Standard Normal Distribution

Reading Z Table - Option 1

Reading Z Table - Option 2

Example 1

Normal Approximation to Binomial Distribution

Example 2

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Random Variables 5

Continuous Random Variables 6

Normal Distribution 1

Normal Distribution 2

Normal Distribution 3

Normal Distribution 4

Normal Distribution 5

Normal Distribution 6

Normal 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

Covariance : Discrete Case

Covariance : Continuous Case 1

Covariance : Continuous Case 2

Exam Like Question 1

Variance of Sums

Example 1

Correlation

Example 2

Exam Like Question 2

Functions of Random Variables

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

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

Derived Distributions 1

Derived Distributions 2

Derived Distributions 3

Derived Distributions 4

Derived Distributions 5

Derived Distributions 6

Derived Distributions 7

Derived Distributions 8

Derived Distributions 9

Markov's Inequality

Proof of Markov's Inequality

Example 1

Chebyshev's Inequality

Example 2

Sample Mean

Sample Variance

Example 3

Law of Large Numbers

Introduction

Example 1

Example 2

Example 3

Example 4

Example 5

Central Limit Theorem 1

Central Limit Theorem 2

Central Limit Theorem 3

Central Limit Theorem 4

Central Limit Theorem 5

Central Limit Theorem 6

Introduction

Recognizing Special Distributions

Example 1

Example 2

Example 3

Example 4

Maximum a Posteriori (MAP) Estimate

Example 5

Example 6

Least Mean Square (LMS) Estimation Without Observation

Example 7

Example 8

Least Mean Square (LMS) Estimation With Observation

Example 9

Example 10

Example 11

LLMS Estimation

Example 12

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

Conditional Probability 1

Conditional Probability 2

Conditional Probability 3

Discrete Joint Distribution 1

Discrete Joint Distribution 2

Discrete Joint Distribution 3

Continuous Random Variables 1

Continuous Random Variables 2

Continuous Random Variables 3

Continuous Random Variables 4

Continuous Joint Probability 1

Continuous Joint Probability 2

Continuous Joint Probability 3

Exponential Distribution

Exponential Distribution 2