CHAPTER 5:Random Variables 5.2 Means and Variances of Random Variable
PICK 3 • You buy a Pick 3 ticket and choose straight play. • How much does it cost? • How much could you win? • What is the probability of winning with that one ticket? • What is the average payoff?
Means • Mean of a DISCRETE Random Variable. • This is sometimes called the expected value. • In the lottery problem, is it possible to win or lose just $.50? • The expected value is often not a possible value of X.
Find the mean of the number of dots that appear when a die is tossed. X P(X) X * P(X)
In a family with three children, find the mean number of children who will be girls. • X P(X)
Class work/ Homework • P. 267 numbers 3, 4, and 5 • ONLY FIND THE MEAN!
Variance • Variance of a DISCRETE Random Variable. • The standard deviation is the square root of the variance.
Variance Find the variance and standard deviation for the number of spots that appear when a die is tossed. (Recall from yesterday that the mean is 3.5) X P(X) X* P(X) X2 * P(X)
Variance • Take a look at problem 2 on page 267…
Means and Variancesof Random Variables • page 267 #1, 6-10
Expected Value • The expected value of a discrete random variable of a probability distribution is the theoretical average of the variable • E(X) = expected value
Example • One thousand tickets are sold at $1 each for a color TV valued at $350. What is the expected value of the gain if you purchase one ticket?
Example 2 A client has two bonds to choose from in which to invest $5000. Bond X pays a return of 4% and has a default rate of 2%. Bond Y pays a 2 ½ % return and has a default of 1%. Find the expected rate of return and decide which bond would be a better investment if the investor loses all the investment when the bond defaults.
Practice • P. 268 14-18