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D Consider an auto insurance portfolio where the number of accidents follows a Poisson distribution with parameter )= 2000. Suppose the damage sizes for individual

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D Consider an auto insurance portfolio where the number of accidents follows a Poisson distribution with parameter )= 2000. Suppose the damage sizes for individual accidents are i.i.d. (independent identically distributed) r.v.'s following a uniform distribution on [0,10]. (Units of money are not specified; it may be $100, or $1000, or something else). Each policy involves a deductible of 2 (units of money). Let N1 be the number of accidents that result in claims, and N2 be the number of accidents that do not result in claims. Answer the following questions 1-5.D Question 1 5 pts Are Ni, Na independent? Depends on a situation, Yes No D Question 2 2 pts What Is the name of the distributions of MI. N2? Gamma O Exponential Compound Poisson Marked PoissonD Question 3 2 pts What is the mean and variance of N? 132968. 1329.48 ( 400 160000' 570.32,670.32 1600, 1400 1600,3200 D Question 4 2 pts What is the mean and variance for No? 0400,400 0 670.32,670.32 137347, 1393.47 O 1600,3200 G 400 16000090 09 D Question 5 5 pts Which of the following numbers is close to the probability that N will not be larger than 1600? (Hint: To what distribution is the Poisson distribution with a parameter of A close for "large" A?) 01 Q:0.75 0 0.25 0 05

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