Math 370X - Quiz 3Saumil PadhyaSeptember 19, 2016Name Net ID1.In modeling the number of claims filed by an individual under an automobile policy during athree-year period, an actuary makes the simplifying assumption that for all integers n≥0,pn+1=15pn, where pnrepresents the probability that the policyholder files n claims duringthe period. Under this assumption, what is the probability that a policyholder files morethan one claim during the period?(A)14(B)27(C)13(D)23(E)342.A group insurance policy covers the medical claims of the employees of a small company.The value, V, of the claims made in one year is described by V = 100,000Y where Y is arandom variable with density function f(y) = k(1-y)4for 0 < y < 1 where k is a constant.What is the conditional probability that V exceeds 40,000, given that V exceeds 10,000?(A) 0.08(B) 0.13(C) 0.17(D) 0.20(E) 0.5113. Let X be a random variable with distribution function F(x) =0 for x < 0x8for 0 ≤ x < 114+x8for 1 ≤ x < 234+x12for 2 ≤ x < 31 for x ≥ 3Calculate P (1 ≤ X ≤ 2).(A)18(B)38(C)716(D)1324(E)19244.The loss due to a fire in a commercial building is modeled by a random variable X withdensity functionf(x) = 0.005(20 − x) for 0 < x < 20Given that a fire loss exceeds 8, what is the probability that it exceeds
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