Chapter 7 Lesson 7.4a Random Variables and Probability Distributions 7.4: Mean and Standard Deviation of a Random Variable

Means and Standard Deviations of Probability Distributions The mean value of a random variable x describes where the probability distribution of x is centered. The standard deviation of a random variable x describes variability in the probability distribution

Mean and Variance for Discrete Probability Distributions Mean is sometimes referred to as the expected value (denoted E(x)). Variance is calculated using Standard deviation is the square root of the variance.

 x = 1.51 pets Dogs and Cats Revisited... Let x = the number of dogs and cats in a randomly selected household in Wolf City x P(x) What is the mean number of pets per household in Wolf City? xP(x) xP(x)

 x 2 = (0-1.51) 2 (.26) + (1-1.51) 2 (.31) + (2-1.51) 2 (.21) + (3-1.51) 2 (.13) + (4-1.51) 2 (.06) + (5-1.51) 2 (.03) = Dogs and Cats Revisited... Let x = the number of dogs or cats per household in Wolf City x P(x) What is the standard deviation of the number of pets per household in Wolf City? First find the deviation of each x- value from the mean. Then square these deviations. Next multiply by the corresponding probability. Then add these values. This is the variance – take the square root of this value.  x = pets

Practice Problem: pg.408: #7.9 1)Find the long-run average number of broken eggs in a carton. 2)Find the variance and standard deviation.

Practice Problem Answers: pg.408: #7.9 1) eggs 2)

Homework Pg.333: #7.28, 29, 33-35, 41 (due in 2 days)