(d) Find the Fisher information for the random sample of the parameter lambda. (e) What is the Cramer Rao Lower bound for an unbiased estimator of the parameter lambda? (f) Is the MLE of part (c) a minimum variance unbiased estimator (MVUE) of lambda

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 Let  random sample from a Poisson distribution with parameter .  A random variable X with Poisson distribution has a probability mass function (pmf) of

p(x; lambda)=((lambda^x)(e^-lambda))/x!, x=0,1,...

with E(X)=lambda  and Var(X)=lambda .

 

(d) Find the Fisher information for the random sample of the parameter lambda.

(e) What is the Cramer Rao Lower bound for an unbiased estimator of the parameter lambda?

(f) Is the MLE of part (c) a minimum variance unbiased estimator (MVUE) of lambda?

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