Math 370X - Quiz 5Saumil PadhyaOctober 10, 2016Name Net ID1. A company prices its hurricane insurance using the following assumptions:(i) In any calendar year, there can be at most 1 hurricane.(ii) In any calendar year, the probability of a hurricane is 0.05.(iii)The number of hurricanes in any calendar year is independent of the number of hurricanesin any other calendar year.Using the company’s assumptions, calculate the probability that there are fewer than 3 hurricanesin a 20-year period.(A) 0.06(B) 0.19(C) 0.38(D) 0.62(E) 0.922.A study is being conducted in which the health of two independent groups of ten policyholdersis being monitored over a one-year period of time. Individual participants in the study dropout before the end of the study with probability 0.2 (independently of the other participants).What is the probability that at least 9 participants complete the study in one of the twogroups, but not in both groups?(A) 0.096(B) 0.192(C) 0.235(D) 0.376(E) 0.46913.An insurance policy on an electrical device pays a benefit of 4000 if the device fails duringthe first year. The amount of the benefit decreases by 1000 each successive year until itreaches 0. If the device has not failed by the beginning of any given year, the probability offailure during that year is 0.4. What is the expected benefit under this policy?(A) 2234(B) 2400(C) 2500(D) 2667(E) 26944.An actuary has discovered that policyholders are three times as likely to file two claims as tofile four claims. If the number of claims filed has a Poisson distribution, what is the varianceof number of claims filed?(A)1√3(B) 1(C)√2(D) 2(E)
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