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
(Hint: F(X) has uniform distribution on (0, 1))
i could not understand the solution.why do we have to consider limits only from 0 to 1?..please help.
Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion
Thanks for solving it.
but i have a doubt !
When we fix 3 at the fourth place such that the arrangement is _ _ _ 3 _ _ _,
then for the first place we will have 4 choices i.e. 1,2,4,5
for the next place we will have 3 choices left,
and consequently 2 choices for the third place.
Moving to the right of 3, we will have 3 choices i.e 6,7 and 4 or 5(depending on which number was put before 3) for the fifth place,
2 choices for the sixth place and the last one will have 1 choice.
So wont it be 4*3*2*3*2, which makes the sum 240?
However the answer given by sir is however 168 contrary to both our answers!!