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CHAPTER 5: Random Variables

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.

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CHAPTER 5: Random Variables

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  1. CHAPTER 5:Random Variables 5.2 Means and Variances of Random Variable

  2. 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?

  3. 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.

  4. Find the mean of the number of dots that appear when a die is tossed. X P(X) X * P(X)

  5. In a family with three children, find the mean number of children who will be girls. • X P(X)

  6. Class work/ Homework • P. 267 numbers 3, 4, and 5 • ONLY FIND THE MEAN!

  7. Variance • Variance of a DISCRETE Random Variable. • The standard deviation is the square root of the variance.

  8. 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)

  9. Variance • Take a look at problem 2 on page 267…

  10. Means and Variancesof Random Variables • page 267 #1, 6-10

  11. 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

  12. 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?

  13. 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.

  14. Practice • P. 268 14-18

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