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

Mean of a discrete random variable Multiply each possible value by its probability, then add all the products x = x1p1 + x2p2 + . . . + xkpk

Variance of a discrete random variable x2 = (x1 - x)2 p1 + (x2 - x)2 p2 + . . . + (xk - x)2 pk x2 = sum(xi - x)2 pi Standard deviation, x = square root of the variance

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

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

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

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

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

Practice Problems pg. 427 #7.42 -7.50 Chapter Review