Math Help - [SOLVED] urgent... i have a question about expectation value.. i need help.

1. [SOLVED] urgent... i have a question about expectation value.. i need help.

Consider a random variable X that takes only nonnegative integer values. Show that the following
is a way of computing the expectation of X:
E(X) = (sum of this function from x=0 to x= infinity) (sum symbol) Pr(X > x)

2. Well, what is $P(X>x)?$

It is the cumulative distribution function. What do you get when you sum over the distribution function for all $x?$ What do you get when you sum over the distribution function to some $x?$

3. I'll just make your life easy.

$\sum_{x=0}^{\infty} P(X>x) = \sum_{j=0}^{\infty}\sum_{x=0}^{j} P(X=j) = \sum_{j=0}^{\infty}jP(X=j) = E[X].$

Note this only necessarily holds for integer-valued non-negative random variates.

4. thanks a lot

it was really important
Originally Posted by Anonymous1
I'll just make your life easy.

$\sum_{x=0}^{\infty} P(X>x) = \sum_{j=0}^{\infty}\sum_{x=0}^{j} P(X=j) = \sum_{j=0}^{\infty}jP(X=j) = E[X].$

Note this only necessarily holds for integer-valued non-negative random variates.