Question

A financial analyst has found that policy holders are four times as likely to file two claims as to file four claims . If the number of claims filed has a poisson distribution , what is variance of the number of claims filed?

Answer 1

Let X be the random number of claims filed by policyholders. We know that the variance of a Poisson distribution is λ. But we have 4P(X = 4) = P(X = 2) that is 4e^-λ (λ⁴/4!)=e^-λ(λ² /2!) ⇒4λ²/4!=1/2 ⇒ λ² = 3⇐⇒ λ =1.732 hence the variance of X is equal to 1.732.