1. The number of days that elapse between the beginning of a calendar year and t
ID: 3362332 • Letter: 1
Question
1. The number of days that elapse between the beginning of a calendar year and the moment a high-risk driver is involved in an accident is considered to be a random variable with the pdf ce. An insurance company expects that 30% of high-risk drivers will be involved in an accident during the first 50 days of a calendar year. What proportion of high-risk drivers are expected to be involved jin an accident during the first 80 days of a calendar year? [A] .37 B] .43 [C].47 D .55 E .64 2. An actuary works on 10 fire and 15 flood claims. Let X denote the number of fire claims in a selection of 10 claims selected at random and with- ut replacement from the considered 25 claims. Find the ratio Var(X)/E(X). [A] 1/8 [B] 3/16 [Cl2/8 [D] 3/8 7/16 3. As part of the underwriting process for insurance, each prospective policyholder is tested for high level of cholesterol. Let X represent the num- ber of tests completed when the first person with high level of cholesterol is found. The expected value of X is 12.5. Calculate the probability that the sixth person tested is the first one with high level of cholesterol. AlQ B043 (C.053 D].078 E .094Explanation / Answer
Solution:
1) Option B) 43
Let T be the number of days that elapse before a high-risk driver is involved in an accident. We know that T is exponentially distributed with unknown parameter . We are also given that
0.3 = Pr(T 50 ) = 1- e-50 .
Therefore, e-50 = 0.7 and
= -ln 0.7/50
It follows that
Pr(T 80) = 1 - e-80 = 1- e 80/50.ln 0.7 = 1- 0.780/50 = 0.435.
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