Question 3: Let X1,..., X.be iid Poisson (2) random variables. a. Find the maximum likelihood estimate...

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Question

Question 3: Let X1,..., X.be iid Poisson (2) random variables. a. Find the maximum likelihood estimate for X. b. Obtain the F

Answer 1

Answer #1

a) MLE :
The pmf of X is f(x)= -,x=0,1,2, Let X1, X2, X, be a random sample of size n is taken from above poisson distribution The lik

b) Fisher Information :

The pmf of X is f(x) = 4*2*,x= 0,1,2,.. The Likelihood function is L= LISO, 2) [1() in L=-natio a – 10 (76531) =-nd+¿x in 2

c) MLE of $\lambda$ is $\overline{x}$

Fisher information I( $\lambda$ ) = 1 / Var(MLE) = 1 / Var( $\overline{x}$ ) = 1 / ( $\lambda$ /n) = n/ $\lambda$

d) Confidence Interval for the parameter : $\lambda$

The pmf of poisson variate is P(X = x) = -,X = 0, 1, 2,... Mean E(X)= È «P(X = *) 1 + 2 + + - 3! +.... 2! B[X*)= 3 XP(X= x) =

Answer 2

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