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## CHAPTER 5: Random Variables

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**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