Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

(b) Recall that X follows a Poisson distribution with mean > > 0 if P(X = k) = e for k 0, 1, 2....

image text in transcribed

(b) Recall that X follows a Poisson distribution with mean > > 0 if P(X = k) = e for k 0, 1, 2.... Now let X1,..., Xm be a sample from the Poisson distribution with (unknown) mean , and Y,..., Y be a sample from the Poisson distribution with (unknown) mean +A. Furthermore, {X1,..., Xm, Y,..., Yn} are independent of each other. i. Find the estimators for and A using method of moments. Are they consistent (as n, m)? Now find the standard errors for the estimators. ii. Find the maximum likelihood estimators for and A. iii. Suppose that m = 40, Xm = 1 X = 10, n = 100 and Yn = n = 11. m Would you reject Ho: A = 0 against H: A0 at the 5% significance level? Would you reject Ho A = 0 against H A > 0 at the 5% significance level? : Briefly comment on your findings. [10 marks for both parts; 20 marks in total]

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image_2

Step: 3

blur-text-image_3

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

An Introduction to Analysis

Authors: William R. Wade

4th edition

132296381, 978-0132296380

More Books

Students also viewed these Mathematics questions

Question

-x/2 x/4 If A = -x/2 and A-1 =6 then x equals

Answered: 1 week ago