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Consider an auto insurance portfolio where the number of accidents follows a Poisson distribution with parameter = 1000. Suppose the damage sizes for individual accidents are i.i.d. (independent identically distributed) r.v.'s following an exponential distribution with parameter a=0.1. Each policy involves a deductible of 5 (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. Finish the following questions: 1-5 Question 1 5 pts Are M1, N2 independent? O True False Question 2 1 pts What is the name of the distributions of N1, N2? Poisson Uniform O Exponential Compound Poisson Question 3 2 pts What is the mean and variance of N1? O 393.47, 393.47 606.53, 606.53 606.53, 367878.64 1000,1000 500,500 Question 4 2 pts What is the mean and variance for N2? 1000,1000 393.47, 154818.64 500,500 606.53, 606.53 O 393.47, 393.47 Question 5 5 pts Which of the following numbers is close to the probability that N2 will not be larger than 393.47? (Hint: To what distribution is the Poisson distribution with a parameter of ) close to for "large" X?) O 0.75 1 O 0.25 O 0.5