1. Section 09

9.  This table is on page 280 of the Actex manual Distribution of XiDistribution of Y Bernoulli B(1,p)Binomial B(k,p) Binomial B(n,p) Geometric pNegative binomial k,p Normal N( μ,σ 2 )  There are more than these but these are the most common/easy to remember

12. The profit for a new product is given by Z = 3X – Y – 5. X and Y are independent random variables with Var(X)=1 and Var(Y)=2. What is the variance of Z? A) 1 B) 5 C) 7 D) 11 E) 16

13. A company has two electric generators. The time until failure for each generator follows an exponential distribution with mean 10. The company will begin using the second generator immediately after the first one fails. What is the variance of the total time that the generators produce electricity?

14. In a small metropolitan area, annual losses due to storm, fire, and theft are assumed to be independent, exponentially distributed random variables with respective means 1.0, 1.5, and 2.4 Determine the probability that the maximum of these losses exceeds 3.

15. An auto insurance company is implementing a new bonus system. In each month, if a policyholder does not have an accident, he or she will receive a $5 cash-back bonus from the insurer. Among the 1000 policyholders of the auto insurance company, 400 are classified as low-risk drivers and 600 are classified as high-risk drivers. In each month, the probability of zero accidents for high-risk drivers is.8 and the probability of zero accidents for low-risk drivers is.9 Calculate the expected bonus payment from the insurer to the 1000 policyholders in one year.