Chapter 9: Random Variables and Distributions

1. Random Variables
2. Discrete Vs Continuous Random Variable
3. Introducing Probability Distribution
4. Probability Distribution of Discrete Random Variable
5. More on Probability Distribution of Discrete Random Variable
6. Problem - Probability Distribution of Discrete Random Variable
7. The Expected Value of Random Variable
8. Use of Expected Value in Decision Making
9. More on Use of Expected Value in Decision Making
10. The PDF of Continuous Distribution
11. More on The PDF of Continuous Distribution
12. Finding Area Under the Curve with Trapezoidal Rule
13. More on Finding Area Under the Curve with Trapezoidal Rule

9.2: The Expectation of Random Variable

1. Expectation
2. Applications of Expectation
3. How Probability Helps Expectations
4. The Expectation of a Discrete Distribution
5. Problem1-The Expectation of a Discrete Distribution
6. Problem2-The Expectation of a Discrete Distribution
7. More on Problem2-The Expectation of a Discrete Distribution
8. Laws of Expectation
9. More on Laws of Expectation
10. Addition and Subtraction Laws of Expectation
11. Multiplication Law of Expectation
12. Problem-Laws of Expectation

9.3: Properties of Variances

1. Properties of Variance1
2. Properties of Variance2
3. Properties of Variance3
4. Properties of Variance4
5. Problem1 - Properties of Variance
6. Problem2 - Properties of Variance

9.4: Sum or Differences of Variances

1. Variance of the Sum or Difference of Two Random Variables1
2. Variance of the Sum or Difference of Two Random Variables2
3. Variance of the Sum or Difference of Two Random Variables3
4. Variance of the Sum or Difference of Two Random Variables4
5. Problem-Variance of the Sum or Difference of Two Random Variables