1. Means and Variances of Random Variables
Section 7.2
Means and Variances of Random Variables

2. Mean of a discrete random variable
Multiply each possible value by its probability, then add all the products
x = x1p1 + x2p xkpk

3. Variance of a discrete random variable
x2 = (x1 - x)2 p1 + (x2 - x)2 p (xk - x)2 pk
x2 = sum(xi - x)2 pi
Standard deviation, x = square root of the variance

4. Law of Large Numbers
As the number of observations increase, the sample mean becomes closer to 

5. Rules for Means
If X is a random variable and a and b are fixed numbers, then a + bx = a + bx
If X and Y are random variables, then x + y = x + y

6.  Correlation of two random variables
Correlation between two independent random variables is 0

7. Rules for Variances 2a+bx = b22x If X and Y are independent, then,
2x+y = 2x + 2y
2x-y = 2x - 2y

8. Rules for Variances 2x+y = 2x + 2y + 2xy
If X and Y have correlation , then
2x+y = 2x + 2y + 2xy
2x-y = 2x + 2y - 2xy

9. Practice Problems pg. 427 #7.42 -7.50 Chapter Review