Finding variance

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 Poisson distribution, what is the variance of the number of claims filed.

Answer 1

P(2) = e^-λ λ²/2!

P(4) = e^-λ λ⁴/4!

P(2)/P(4) = e^-λ λ²/2!/(e^-λ λ⁴/4!) = 12/λ²

If P(2)/P(4) = 4, 4 = 12/λ²

Then, 4λ² = 12, or λ = √3

λ is both the mean and variance of the Poisson.

The variance is √3