Estimation ad confidence Interval Q2

**ADARSH** · March 30th 2009, 11:36 PM

These questions are on behalf of Bill who needs urgent help but cant start threads/post for some reasons

Question 1 : Suppose that

$X_1 , X_2,...X_n \color{red}--\color{black}^{iid} N(\mu , \sigma^2)$

Consider the following estimators for $\sigma^2$ .

$S^{*2} =\sum_{i=1}^{n}(\frac{(X_i - \overline X)^2}{n})$ and

$S^2 = \sum_{i=1}^{n}\frac{(X_i - \overline X)^2}{n-1}$

Calculate MSE of those estimators and discuss which one is closer to

$\sigma^2$ .

HINT: If $Z_1 , Z_2,...Z_n \color{red}--\color{black}^{iid} N(0 , 1)$

than

$\sum_{i=1}^{n} (Z_i-\overline{Z})^2 \color{red}--\color{black} {\chi}^2_{n-1}$

Note: MSE - Mean squared Error

iid = independent and identically distributed

--= ~ and iid is above it

**ADARSH** · March 30th 2009, 11:59 PM

The question 2 of the attachment, Can't type now , Sorry, again this is also for Bill

**matheagle** · March 31st 2009, 05:34 PM

${(n-1)S^2\over \sigma^2}$ is a $\chi^2$ random variable with n-1 degrees of freedom.

Hence $S^2$ is unbiased for $\sigma^2$ .

The variance of a $\chi^2$ random variable with n-1 degrees of freedom is 2(n-1).

**polyluka15** · April 1st 2009, 11:18 AM

Please help with both questions, I have the same problem set, and it looks Japanese to me!!!
The Gamma one is very hard.
Please any help!!!!

**mr fantastic** · April 1st 2009, 03:38 PM

Originally Posted by polyluka15

Please help with both questions, I have the same problem set, and it looks Japanese to me!!!
The Gamma one is very hard.
Please any help!!!!

So where are you stuck? What part of matheagle's reply do you need clarification on? What have you tried?

**polyluka15** · April 1st 2009, 06:39 PM

There is question #2 about the Gamma distribution.
a) its a F-distribution where
Z=(X/k) over (Y/m), but in this question I dunno what k and m are??? and even if Z is correct

b) NO CLUE

c) I found this:

Estimate + - (critical value)*(standard error)

where the critical value comes from the relevant distribution e.g. Normal, t, chi-square, F, Gamma, and so on.

However, the standard error will vary depending on statistic being estimated.

Of which I don't know what is what.

Am I out of it? I have little idea of what is going on

**polyluka15** · April 2nd 2009, 07:03 AM

ill tell y teacher its unsolvable, none of the ta's i called in toronto, could help.

**mr fantastic** · April 2nd 2009, 08:39 PM

Originally Posted by polyluka15

ill tell y teacher its unsolvable, none of the ta's i called in toronto, could help.

This thread is relavant to question 2: http://www.mathhelpforum.com/math-he...on-ratios.html

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Estimation ad confidence Interval Q2

Estimation ad confidence Interval Q2

HELP with POSTED assignment (Both questions by Bill)

thats sad

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