**Problem 3: Poisson Distribution in Insurance Claims**Assume that a policyholder is sixteen times more likely to file exactly two claims than to file exactly four claims in one year.Let $ X $ be the number of claims in a year, where $ X \sim \text{Poisson}(\lambda) $.Tasks:- (a) Find $\lambda$.- (b) Calculate $\Pr(X \geq 2)$.- (c) Determine the expected value $E(X!)$.

given data x follows poisson distribution P(x=X) = e-λ(λ)xx! P(x=2) = 16P(x=4)

Answered: a) 3. Assume that a policyholder is…

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a) 3. Assume that a policyholder is sixteen times more likely to file exactly two claims as to file exactly four claims in one year. Let X be the number of claims in a year and X~ Poisson (X). (a) Find X (b) Pr(X > 2) 16 (c) E(X!)