Find the method of moments (MOM) estimator of lambda. (b) Find a sufficient statistic for lambda. (c) Find the maximum likelihood estimator (MLE) of lambda. (Remember that you already found an expression for the joint pmf in

Find the method of moments (MOM) estimator of lambda. (b) Find a sufficient statistic for lambda. (c) Find the maximum likelihood estimator (MLE) of lambda. (Remember that you already found an expression for the joint pmf in

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 30E

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Question

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 .

(a) Find the method of moments (MOM) estimator of lambda.

(b) Find a sufficient statistic for lambda.

(c) Find the maximum likelihood estimator (MLE) of lambda. (Remember that you already found an expression for the joint pmf in part (b).)

(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?

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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