Math 370X - Quiz 7Saumil PadhyaOctober 24, 2016Name Net ID1.A company offers earthquake insurance. Annual premiums are modeled by an exponentialrandom variable with mean 2. Annual claims are modeled by an exponential random variablewith mean 1. Premiums and claims are independent. Let X denote the ratio of claims topremiums, and let f be the density function of X. Determine f(x), where it is positive.(A)12x + 1(B)2(2x + 1)2(C) e−x(D) 2e−2x(E) xe−x2.A company offers a basic life insurance policy to its employees, as well as a supplemental lifeinsurance policy. To purchase the supplemental policy, an employee must first purchase thebasic policy. Let X denote the proportion of employees who purchase the basic policy, and Ythe proportion of employees who purchase the supplemental policy. Let X and Y have thejoint density function f(x,y) = 2(x + y) on the region where the density is positive.Given that 10% of the employees buy the basic policy, calculate the probability that fewer than5% buy the supplemental policy.(A) 0.010(B) 0.013(C) 0.108(D) 0.417(E) 0.50013.An insurance company sells automobile liability and collision insurance. Let X denote thepercentage of liability policies that will be renewed at the end of their terms and Y thepercentage of collision policies that will be renewed at the end of their terms. X and Y havethe joint cumulative distribution functionF (x, y) =xy(x + y)2, 000, 000, 0 ≤ x ≤ 100, 0 ≤ y ≤ 100.Calculate Var(X).(A) 764(B) 833(C) 3402(D) 4108(E) 41674.A company is reviewing tornado damage claims under a farm insurance policy. Let X be theportion of a claim representing damage to the house and let Y be the portion of the sameclaim representing damage to the rest of the property. The joint density function of X and Yisf(x, y) = 6[1 − (x + y)], x > 0, y > 0, x + y < 1Calculate the probability that the portion of a claim representing damage to the house is lessthan 0.2.(A) 0.360(B) 0.480(C) 0.488(D) 0.512(E)
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