291. Let X and Y be discrete random variables with joint probability function

  Calculate Corr (X, Y), the correlation coefficient of X and Y.
(A) 0.06
(B) 0.23
(C) 0.26
(D) 0.38
(E) 0.63

292. Let X and Y be discrete random variables with joint probability function Calculate the variance of Y. (A) 1.67 (B) 2.22 (C) 3.33 (D) 5.00 (E) 5.56

293. A company provides disability benefits to its employees. There are only two possible benefits: partial disability, costing the company 40, and total disability, costing the company 200. The company employs a number of married couples. Let (X,Y) denote the company's disability costs for a randomly selected employed married couple. The joint probability function for (X,Y) is:  Calculate the standard deviation of the total disability cost X + Y for the married couple. (A) 12.3 (B) 13.8 (C) 15.7 (D) 16.6 (E) 19.8

294. The probability that the economy will improve, remain stable, or decline is:    Prices for Stock X and Stock Y will change as follows:   Determine which of the following statements about the percentage price changes for Stock X and Stock Y is true. (A) The percentage change for Stock X has a larger variance and a larger mean. (B) The percentage change for Stock X has a larger variance and the means are equal. (C) The percentage change for Stock X has a larger variance and a smaller mean. (D) The variances are equal and the percentage change for Stock X has a larger mean. (E) Both the variances and the means are equal.

295. A company is marketing an investment opportunity to four potential customers. The company believes that its probability of making a sale is 0.5 for each of the first three customers but that it is only 0.1 for the fourth customer. The customers' purchases are independent of one another. Calculate the probability that at most two customers purchase the investment. (A) 0.38 (B) 0.46 (C) 0.54 (D) 0.84 (E) 0.90

296. An actuary compiles the following information about a portfolio of life insurance policies: i) There are 150 more policies on males than there are on females. ii) There are 100 more policies on female nonsmokers than there are on male nonsmokers. iii) There are 350 policies on smokers. Calculate the number of policies on female smokers within this portfolio. (A) 50 (B) 100 (C) 200 (D) 250 (E) 300

297. The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function f, where f (x) is proportional to . Calculate the probability that the lifetime of the machine part is less than five. (A) 0.03 (B) 0.13 (C) 0.42 (D) 0.58 (E) 0.97

298. The claim, X, for a dental insurance policy is a random variable with the following probability function:The premium for the policy is equal to 125% of the expected claim amount. Calculate the approximate probability that the total claims on 76 independent policies exceed the total premium collected. (A) 0.02 (B) 0.07 (C) 0.17 (D) 0.25 (E) 0.40

299. An insurance company categorizes its policyholders into three mutually exclusive groups. A study produced the following information:  Within each group, the numbers of claims made by individual policyholders are mutually independent Poisson random variables. Calculate the expected total number of claims, in thousands, made by the 100,000 policyholders. (A) 21 (B) 28 (C) 36 (D) 64 (E) 72

300. A group of insurance policies have all been in force for at least three years. The insurance company plans to pay a dividend on each policy in the group that had no more than one claim incurred on it in the past three years. The number of claims incurred on a policy in any year follows a Poisson distribution with mean 0.288 and the number incurred in any year is independent of the number incurred in any other year. Calculate the probability that a policy chosen at random from the group will receive a dividend. (A) 0.01 (B) 0.36 (C) 0.42 (D) 0.54 (E) 0.79

301. An insurance company sells a one-year insurance policy that covers fire and theft losses. The variance of the number of fire losses is 5. The variance of the number of theft losses is 8. The covariance between the number of fire and theft losses is 3. Calculate the variance of the total number of fire and theft losses covered by this policy. (A) 7 (B) 10 (C) 13 (D) 16 (E) 19

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