Question

(a) Let Y1,Y2,··· ,Yn be i.i.d. with geometric distribution P(Y = y) = p(1−p)y-1 y=1, 2,...

(a) Let Y1,Y2,··· ,Yn be i.i.d. with geometric distribution P(Y = y) = p(1−p)y-1 y=1, 2, ........, 0<p<1. Find a sufficient statistic for p.

(b) Let Y1,··· ,yn be a random sample of size n from a beta distribution with parameters α = θ and β = 2. Find the sufficient statistic for θ.

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