# Thread: I have questions ??

1. ## I have questions ??

Hi

I have 3 questions.

Let x1, . . . , xn be independent observations of a chi-square(k) random variable, with p.d.f.
f(x)= 1/(2^k/Γ(k/2)) x^(k/2-1) exp(-x/2)

I have found E(X)=k , Var(X)= 2k, the method of moments estimator for k which is (k*) = Xbar
and k* is unbiased of k because E(k*)=E(Xbar)=1/n [E(X1)+E(X2)+...+E(Xn)]= 1/n nk= k

My questions are:
1. How can I find Var(k*) ?
2. Show that the Cram´er-Rao lower bound for the variance of unbiased estimators of k is 4[n(d^2/d ��^2)logΓ(��) (k/2)]^-1
3. show that k* is approximately fully efficient.

Many thanks in advance.

2. ## Re: I have questions ??

Just by definition

For part b, I do not know what is your problem. Maybe you try
to begin with the definition and work with that first.

http://en.wikipedia.org/wiki/Cram%C3...80%93Rao_bound

I guess part c) is just asking you to compare the answer you obtained
in part a) and b). If they are close, then the estimator is approximately
efficient.

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