Answer to Question #116157 in Statistics and Probability for Emmanuel

Question

A financial analyst has found out that policyholders are four times as likely to file two
claims as to file four claims. If the number of claims filed has a posson 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