Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

Posted by soumen08 on Jun 21, 2014; 6:12am
URL: http://discussion-forum.276.s1.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p7593246.html

Dreyfus wrote

@soumen...actually u r not applying the var formula correctly
Var(mean of Xs) =( 1/n²)( varx1 + varx2 + varx3+........varxn+ sum of all covariance terms)
Sum of all covariance pair is equal to n(n-1)*p as all cov b/w diff pairs of x's are same.
And sum of variances is equal to n*sigma²
So Var (mean of Xs) = (1/n²)*(n*sigma² + n(n-1)*p)

Thanks Dreyfus! I understand that now. I was considering (wrongly) that the variance of the mean is the mean of the variance. The n^2 is what I had missed.

Can you help me with this question?

Consider the following 2-variable linear regression where the error e(i)’s are independently and identically distributed with mean 0 and variance 1; y(i) = a + b(x(i) − Mean(x)) + e(i), i = 1, 2, . . . , n. where Mean(x) = (x(1) + x(2) + ....x(n))/n
Let a^ and b^ be ordinary least squares estimates of a and b respectively.
Then the correlation coefficient between a^ and b^ is
(a) 1,
(b) 0,
(c) −1,
(d) 1/2.

How is the answer zero?