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(Solved): Suppose a random sample x_(1),x_(2),dots,x_(n) follows a Poisson distribution with a mean \lambda . ...
Suppose a random sample x_(1),x_(2),dots,x_(n) follows a Poisson distribution with a mean \lambda .
f_(x)(x)=\lambda ^(x)(e^(-\lambda ))/(x!),x=0,1,2,3,dots
a. Show that \bar{x} is an (i) unbiased, (ii) consistent, and (iii) sufficient estimator of \lambda .
b. Using the Cramer-Rao Lower Bound of Poisson Distribution, show that \bar{x} is an MVUE
of \lambda .