Answer to Question #115434 in Statistics and Probability for Fauziya

Question

A financial analyst has found out that policy holders are four times as likely to file two claims as to file four claims.If the number of claims filed has Poisson distribution,What is the 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.