i)only Let (X1,...,Xn), n ≥ 2, be a random sample from a distribution with discrete probability density fθ,j,whereθ ∈ (0,1), j = 1, 2, fθ,1 is the Poisson distribution with mean θ,andfθ,2 is the binomial distribution with size 1 and probability θ. (i) Show that T = ni=1Xi is not sufficient for (θ,j).

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Let (X1,...,Xn), n ≥ 2, be a random sample from a distribution with discrete probability density fθ,j,whereθ ∈ (0,1), j = 1, 2, fθ,1 is the Poisson distribution with mean θ,andfθ,2 is the binomial distribution with size 1 and probability θ. (i) Show that T = ni=1Xi is not sufficient for (θ,j).

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