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2 Let X1Xn be a random sample from Poisson distribution P.pdf

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2. Let X1,,Xn be a random sample from Poisson distribution P(),>0. (1) (10 points) Find a complete sufficient statistic for . (2) (15 points) Find the UMVUE of P(X1=0)=exp(). (Hint: I(X1=0) is an unbiased estimator of exp() ). (3) (15 points) Find the CFR lower bound for all unbiased estimators of exp()..

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2. Let X1,,Xn be a random sample from Poisson distribution P(),>0. (1) (10 points) Find a complete sufficient statistic for . (2) (15 points) Find the UMVUE of P(X1=0)=exp(). (Hint: I(X1=0) is an unbiased estimator of exp() ). (3) (15 points) Find the CFR lower bound for all unbiased estimators of exp().

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2 Let X1Xn be a random sample from Poisson distribution P.pdf

  • 1. 2. Let X1,,Xn be a random sample from Poisson distribution P(),>0. (1) (10 points) Find a complete sufficient statistic for . (2) (15 points) Find the UMVUE of P(X1=0)=exp(). (Hint: I(X1=0) is an unbiased estimator of exp() ). (3) (15 points) Find the CFR lower bound for all unbiased estimators of exp().