Consider an auto insurance portfolio where the number of accidents follows a Poisson distribution with parameter lamda = 1000. Suppose the damage sizes for separate accidents are i.i.d. (independent identically distributed) r.v.'s having an exponential distribution with a mean of $2500. Each policy involves a deductible of $500. 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. 1. Are N1, N2 dependent? 2. What is the name of the distributions of N1, N2? Compound Poisson or Marked Poisson? 3. What is the mean and variance of N1?
Consider an auto insurance portfolio where the number of accidents follows a Poisson distribution with parameter lamda = 1000. Suppose the damage sizes for separate accidents are i.i.d. (independent identically distributed) r.v.'s having an exponential distribution with a mean of $2500.
Each policy involves a deductible of $500. 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.
1. Are N1, N2 dependent?
2. What is the name of the distributions of N1, N2? Compound Poisson or Marked Poisson?
3. What is the mean and variance of N1?
4. What is the mean and variance of N2?
5. Which of the number is close to the probability that N1 will not be larger than 790? (Hint: to what distribution is the Poisson distribution with a parameter of lamda close for "large" lamda's?
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