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

Posted by Amit Goyal on Apr 13, 2010; 5:27am
URL: http://discussion-forum.276.s1.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p4894317.html

The sum C(n+0, 0) + C(n+1, 1) +............C(n+m, m)equals
(a) C(n+m+1, n+m),
(b) (n+m+1)C(n+m, n+1),
(c) C(n+m+1, n),
(d) C(n+m+1, n+1).

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.