Question

Consider a large insurance company with two types of policies: policy A and policy B. Suppose that the number of claims the company sees in a given day has a Poisson distribution with a parameter of lamda. Suppose further that a randomly selected claim is from a type A policy with probability p. Find the probability that the company will receive exactly k claims from A policies tomorrow.

Answer 1

Probability that selected claim is from type A = p

Poisson distribution with parameter $\lambda$

From poisson distribution, P(k events in an interval) is given by

$P(k) = e^{-\lambda } \times \frac{\lambda ^{k}}{k!}$

Thus, total Probability = $e^{-\lambda } \times \frac{\lambda ^{k}}{k!}\times p$