1. ## Estimation ad confidence Interval Q2

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

Question 1 : Suppose that

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

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

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

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

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

$\displaystyle \sigma^2$.

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

than

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

Note: MSE - Mean squared Error

iid = independent and identically distributed

--
= ~ and iid is above it

2. ## Estimation ad confidence Interval Q2

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

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

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

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

4. ## HELP with POSTED assignment (Both questions by Bill)

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

5. 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.
So where are you stuck? What part of matheagle's reply do you need clarification on? What have you tried?

6. 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