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# If the probability that ruin occurs in the first 2

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If the probability that ruin occurs in the first 2 years is 0.2025, find a and b. (Ans: a = 0.05 and b = 0.15) 4. A community is able to obtain plasma at the continuous rate of 100 units per day. The daily demand for plasma is modelled by a com- pound homogeneous Poisson process, where the number of units need- ing plasma has the parameter λ = 20 and the number of units needed by each person is approximated by a distribution defined by the fol- lowing pdf: f ( x ) = e - x/ 3 / 12 + 3 e - x/ 5 / 20 , x > 0 and 0 otherwise. 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. 5. An insurance company’s claims follow a compound homogeneous Pois- son surplus process where the individual claims have a uniform distri- bution over (0,15). The relative security loading is 0.2 and the initial surplus is 50. 1

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(a) Find the pdf for the amount of loss when the surplus falls below the initial fund for the first time. (b) Calculate the probability that the surplus will fall below 40 when it first falls below 50. 6. An insurer’s claims follow the classical risk model where the homoge- neous Poisson process has the rate equal to λ , the claim amounts are uniformly distributed over (0, 10) and the continuous premium rate is 8 per period. If the adjustment coefficient is 0.4, calculate λ . 7. Customers arrive at a store according to a non-homogeneous Poisson process with intensity function λ ( t ) = 3 + 3 t , 0 t 8, where the time t is measured in hours from 12:00 pm. (a) Calculate the probability that the 10th customer inter-arrival time is larger than 30 minutes, given that the 9th customer ar- rived at 14:00.
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• Winter '17
• Ionica Groparu
• Normal Distribution, Probability theory, \$1,000, Compound Poisson process, Compound Poisson distribution

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