Insurance Claims: An insurance company has 1000 policyholders, each of whom will

Question

Insurance Claims: An insurance company has 1000 policyholders, each of whom will independently present a claim in the next month with probability 0.05. Assuming that the amounts of the claims made are independent exponential random variables with mean $800, use simulation to estimate the probability that the sum of these claims exceeds S50,000 in the next month. Estimate the wanted probability using the relative frequency for the claims to exceed $50,000 in a large sample of size 10,000. Estimate also the mean of the sum of these claims. Hint: Use rexp(n,1ambda) to get a sample of size n from the exponential distribution X~Exp(A) with parameter lambda A. Note that the mean is the reciprocal of the rate: E(X)-Answer: 10.7% for the probability, $40K for the clains rnean.

Explanation / Answer

R code :

> sample=rexp(1000,1/800)
> for(i in 1:1000)
+ {
+ if(sample[i]>50000)
+ {
+ x=x+1
+ }
+ }

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