Re: Simple doubt on Expectations (Probability)

Posted by knowpraveen on Jun 06, 2016; 7:33am
URL: http://discussion-forum.276.s1.nabble.com/Simple-doubt-on-Expectations-Probability-tp7601231p7601233.html

By me?

E(X|X<=x)

So, lets say F(y)= P(X<=y|X<=x) = y/x.
Therefore, the density would be f(y)=1/x

The expectation would be integral(y(1/x)) from 0 to x. Hence, the answer comes to be at x/2.

The answer is consistent with intuition, because, for X less than or equal to x, expectation should be the mean of x and 0 i.e x/2. Or, the expectation shouldn't be greater than 1 since x lies between 0 and 1. For all other options, the expectations might exceed 1 for some values of x belongs to (0,1)

What do you say about this?