# expected value of a segment of normal distribution

• Apr 18th 2007, 11:51 PM
fio_2001
expected value of a segment of normal distribution
I need to find the expected value of a segment (namely the segment -infinity to C) of the normal distribution (the bell curve).

i know what i should integrate, I just cant integrate it as it is much too complicated for my small mind to handle.

basically Integral from -infinity to C of x times f(x) dx where f(x) is the pdf of the normal distribution which is much too complicated to write out on a board like this...

thanks a ton if you can get me this !
Norman
• Apr 19th 2007, 11:00 AM
CaptainBlack
Quote:

Originally Posted by fio_2001
I need to find the expected value of a segment (namely the segment -infinity to C) of the normal distribution (the bell curve).

i know what i should integrate, I just cant integrate it as it is much too complicated for my small mind to handle.

basically Integral from -infinity to C of x times f(x) dx where f(x) is the pdf of the normal distribution which is much too complicated to write out on a board like this...

thanks a ton if you can get me this !
Norman

integral_{x=-infty to C} x/sqrt(2 pi) exp(-x^2/2) dx

now d/dx exp(-x^2/2) = -x exp(-x^2/2), so:

integral_{x=-infty to C} x/sqrt(2 pi) exp(-x^2/2) dx = [1/sqrt(2 pi)] [-exp(-C^2/2)]

RonL