CT3 Sep 2006 Q 8(ii)

why I can not write "sample_mean2-alfa*sample_mean2 instead" instead of
"(1-alfa)sample_mean2" specially to find out the mean square error of W.

 

It seems wrong.
can you post what you thought behind writing, sample_mean2-alfa*sample_mean2 instead. ?

 

I just opened the bracket in "(1-alfa)sample_mean2". Not understook what is wrong in it.

 

Okay! you meant as \(var({\bar X_1}+{\bar X_2}-\alpha{\bar X_2}) \) It is correct........
you will get same MSE.

 

No. I am getting different MSE. To calculate MSE, first we have to calculate variance of predictor and

As per suggested solution (which is done without opening bracket)
variance of predictor = (1-alfa)^2 sigma^2/n

whereas if i open the bracket then
Variance of predictor = (1-alfa^2) sigma^2/n

 

\(Var({\bar X_1}+{\bar X_2}-\alpha{\bar X_2})=Var({\bar X_1})+Var({\bar X_2})+\alpha^2*Var({\bar X_2})-2\alpha*Cov({\bar X_2},{\bar X_2}) \)
\(=\sigma_1^2/n+\sigma_2^2/n+\alpha^2*\sigma_2^2/n-2\alpha*\sigma_2^2/n \)

factorize it.

 

Oh! got it. Thanks

Var(sample_mean2-alfa*sample_mean2)=Var(sample_mean2) + Var (alfa*sample_mean2) - Cov(sample_mean2,alfa*sample_mean2)

In your reply I get [Math Processing Error]. How to resolve it ?

once again thanks.

 

refresh page/update browser.....
I use Mozilla Firefox, it shows Math script well.

 

Thanks