Hi,

given that: .

I want to show that

However, when i reached: , i was puzzled on finding ?

Since which variance should I use, s.r.s or i.i.d?

or maybe is there any better way to prove it?

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- Aug 22nd 2009, 06:08 AMnoob mathematicianProving question
Hi,

given that: .

I want to show that

However, when i reached: , i was puzzled on finding ?

Since which variance should I use, s.r.s or i.i.d?

or maybe is there any better way to prove it? - Aug 22nd 2009, 07:18 AMRandom Variable
is (chi-square distriubtion with (n-1) degrees of freedom)

If you want to try and prove that statement, use the fact that and are independent.

So

since the expected value of a chi-square distribution with k degrees of freedom is k - Aug 23rd 2009, 04:58 AMnoob mathematician
Hi tks for the reply.

In addition to this, I've read book stating that the best estimator is as compared to this answer showing that .

Any explaination for this? - Aug 23rd 2009, 08:23 AMRandom Variable
Here's a much better proof that doesn't involve knowing anything about the chi-square distribution:

so

then