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Competitive Stats
Q15Section I (Objective (Q1–Q80))15 of 80

Distribution Theory — conditional MGF from a two-way pmf table

Consider the following for the next three (03) items that follow: The joint pmf of two random variables X and Y is given below (with 0<θ<10<\theta<1): row X=-1 has values θ,2θ,3θ,θ,θ\theta,2\theta,3\theta,\theta,\theta; row X=0 has values 2θ,3θ,θ,0,02\theta,3\theta,\theta,0,0; row X=1 has values θ,θ,θ,θ,2θ\theta,\theta,\theta,\theta,2\theta, for Y =−2,−1,0,1,2=-2,-1,0,1,2 respectively. What is the moment generating function of X∣Y=2X \mid Y = 2?

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