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Competitive Stats
Q46Section I (Objective (Q1–Q80))46 of 80

Distribution Theory — variance of compound Poisson variable

Consider the following for the next three (03) items: Let random variables XX and YY be independently distributed as Poisson (λ)(\lambda) and their moment generating functions together with random variable ZZ satisfy the following relation MZ(t)=MY(log⁡MX(t))M_Z(t) = M_Y(\log M_X(t)) for some t∈(−h,h)t \in (-h, h); h>0h > 0. What is the value of Var⁡(Z)\operatorname{Var}(Z)?

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