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

Posted by Amit Goyal on Apr 11, 2010; 1:59am
URL: http://discussion-forum.276.s1.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p4884146.html

Do the next two then,

Let X be a Normally distributed random variable with mean 0 and variance 1. Let F(.) be the cumulative distribution function of the variable X. Then the expectation of F(X) is
(a) −1/2 ,
(b) 0,
(c) 1/2 ,
(d) 1.

Consider any finite integer r ≥ 2. Then lim(x→0) f(r, x)/a(x) equals,
(where f(r, x) = log(e)(Σ(0, r) (x^k)); and a(x) = Σ(1, ∞) ((x^k)/k!))
(a) 0,
(b) 1,
(c) e,
(d) log(e)2.

Note: Σ(a, b) g(k) is summation of g(k) over values of k from a to b
x^k is x to the power k