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Homework_Assignment_18 - claim amount paid by time t(iv The...

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Homework Assignment 18: For a claim number process {N(t), t 0}, you are given that the waiting times between successive claims are independent and identically distributed with distribution function F(t) = 1 – e -2t . Determine the probability that exactly 3 claims will occur in an interval of length 1.5. (Ans 0.224) Taxicabs leave a hotel with a group of passengers at a Poisson rate λ = 10 per hour. The number of people in each group taking a cab is independent and has the following probabilities: Number of People Probability 1 0.60 2 0.30 3 0.10 Using the normal approximation, calculate the probability that at least 1050 people leave the hotel in a cab during a 72-hour period. (Ans 0.75) A special purpose insurance company is set up to insure one single life. The risk consists of a single possible claim. (i) The claim amount distribution is : Amount Probability 100 0.60 200 0.40 (ii) The probability that the claim does not occur by time t is 1 / (1 + t). (iii) The insurer’s surplus at time t is U(t) = 60 + 20t – S(t), where S(t) is the aggregate
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Unformatted text preview: claim amount paid by time t. (iv) The claim is payable immediately. Calculate the probability of ruin. (Ans ¾) (1) An insurer’s claims follow a compound Poisson claims process with two claims expected per period. Claim amounts can be only 1, 2 or 3 and these are equal in probability. Calculate the continuous premium rate that should be charged each period so that the adjustment coefficient will be 0.5. (Ans 7.8) (2) A community is able to obtain plasma at the continuous rate of 22 units per day. The daily demand for plasma is modeled by a compound Poisson process where the number of people needing plasma has mean 20 and the number of units needed by each person is approximated by an exponential distribution with mean 1. Assume all plasma can be used without spoiling. At the beginning of the period there are 20 units available. Calculate the probability that there will not be enough plasma at some time. (Ans 0.148)...
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