These questions in the attached file have a short deadline. I need a clear flow of the workings that will prove how you arrived at the final answer.
acs_questions.docx
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1. Subway trains arrive at a station at a Poisson rate of 20 per hour. 25% of the trains are express
and 75% are local. The types of each train are independent. An express gets you to work in 16
minutes and a local gets you there in 28 minutes. You always take the first train to arrive. Your
co-worker always takes the first express. You both are waiting at the same station. Which of the
following is true? (A) Your expected arrival time is 6 minutes earlier than your co-worker’s. (B)
Your expected arrival time is 4.5 minutes earlier than your co-worker’s. (C) Your expected arrival
times are the same. (D) Your expected arrival time is 4.5 minutes later than your co-worker’s. (E)
Your expected arrival time is 6 minutes later than your co-worker’s.
2. For a stop-loss insurance on a three person group: (i) Loss amounts are independent. (ii) The
distribution of loss amount for each person is: Loss Amount Probability 0 0.4 1 0.3 2 0.2 3 0.1 (iii)
The stop-loss insurance has a deductible of 1 for the group. Calculate the net stop-loss premium.
(A) 2.00 (B) 2.03 (C) 2.06 (D) 2.09 (E) 2.12
3. A company insures a fleet of vehicles. Aggregate losses have a compound Poisson distribution.
The expected number of losses is 20. Loss amounts, regardless of vehicle type, have exponential
distribution with θ= 200. In order to reduce the cost of the insurance, two modifications are to
be made: (i) a certain type of vehicle will not be insured. It is estimated that this will reduce loss
frequency by 20%. (ii) a deductible of 100 per loss will be imposed. Calculate the expected
aggregate amount paid by the insurer after the modifications. (A) 1600 (B) 1940 (C) 2520 (D)
3200 (E) 3880
4. 124. For a claims process, you are given: (i) The number of claims
m rN t tb g, ≥ 0 is a
nonhomogeneous Poisson process with intensity function:
λ( ) ,,,
t
ttt = ≤ < ≤ < ≤
R|S|T 1 0 1 2 1 2 3 2 (ii) Claims amounts Y are independently and identically distributed
i
random variables that are also independent of N( ) .t (iii) Each Yi is uniformly distributed on
[200,800]. (iv) The random variable P is the number of claims with claim amount less than 500
by time t = 3. (v) The random variable Q is the number of claims with claim amount greater than
500 by time t = 3. (vi) R is the conditional expected value of P, given Q = 4.
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