9: Consider a large insurance company with two types of policies: policy A and p
ID: 3046471 • Letter: 9
Question
9: Consider a large insurance company with two types of policies: policy A and policy B. Suppose that the number of claims the company sees on a given day has a Poisson distribuition with parameter 12. Suppose further that a randomly selected claim is from a type A policy with probaiblity 1/4 .
(a) Find the probaility that the company will recieve at leats 5 claims from A policies tomorrow.
(b) Find the probability that the company will recieve at least 10 total claims tomorrow.
Additionally, suppose that a randomly selected claim from policy A has a 4/5 chance of being greater than 100000 dollar and that a randomly selected claim from policy B has a 1/5 chance of being over 100000 dollar.
(c) Find the expected number of claims over 100000 dollar tomorrow.
(d) Find the probability that there will be less than or equal to 2 claims over 100000 dollar tomorrow.
Explanation / Answer
(a) Here expected number of claimes company will see from type A = 12 * 1/4 = 3
If X is the number of claims from A policies tomorrow.
Pr(X >=5) = POISSON (X 5 ; 3) = 1 - POISSON (X < 5 ; 3) = 1 - 0.8153 = 0.1847
(b) Here if Y is the number of claims recieved tomorrow.
Expected number of claims received tomorrow = 12
Pr(Y 10 ; 12) = POISSON (Y 10 ; 12) = 1 - POISSON (X < 10 ; 12) =1 - 0.2424 = 0.7576
(c) Here expected number of claims over 100000 dollar tomorrow = 12 * 1/4 * 4/5 = 12/5 = 2.4
(d) If Z is the number of claims over 100000 dollar tomorrow.
Pr(Z 2) = POISSON ( Z 2 ; 2.4) = 0.5697
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