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Hey guys
I've been working on my statistic assignment. This is the last question but I don't understand the question. If anyone could help me, I would appreciate. Here is the question
Let X1,...,Xn be a random sample from Poisson(lambda).
(a) Let theta=P(X=1)=lambda*exp(-lambda). Find the UMVUE of theta.
(b) Find the MLE of theta and the approximate distribution of MLE when n is large.
(c) Based on the approximate pivotal in part (b), find a 100(1-a)% confidence interval for theta.
(d) Using the 25 numbers (10,7,8,13,8,9,5,7,6,8,3,6,6,3,5,5,8,10,6,2,10,4,8,6,11), estimate theta using both UMVUE and MLE.
For part(a) and (b), I know how to get the UMVUE and MLE, etc (It is pretty straight forward if I need to get UMVUE/MLE with lambda.). I don't think this is a hard question. But the new parameter, theta, is giving me so much confusion and I have no clue.
Please help me. Thank you.
I've been working on my statistic assignment. This is the last question but I don't understand the question. If anyone could help me, I would appreciate. Here is the question
Let X1,...,Xn be a random sample from Poisson(lambda).
(a) Let theta=P(X=1)=lambda*exp(-lambda). Find the UMVUE of theta.
(b) Find the MLE of theta and the approximate distribution of MLE when n is large.
(c) Based on the approximate pivotal in part (b), find a 100(1-a)% confidence interval for theta.
(d) Using the 25 numbers (10,7,8,13,8,9,5,7,6,8,3,6,6,3,5,5,8,10,6,2,10,4,8,6,11), estimate theta using both UMVUE and MLE.
For part(a) and (b), I know how to get the UMVUE and MLE, etc (It is pretty straight forward if I need to get UMVUE/MLE with lambda.). I don't think this is a hard question. But the new parameter, theta, is giving me so much confusion and I have no clue.
Please help me. Thank you.