# Math Help - integration in probability

1. ## integration in probability

how to integrate x(1/sqrt(2pi))(exp(-(x-y)^2/2)) with respect to x from infinity to infinity? the answer is y. but how do you get that?

2. This integral is the mean of X. When $X\sim N(Y,1)$.

You can let $Z=X-Y\sim N(0,1)$.

There are many ways to show that $\int_{\infty}^{\infty}z e^{-z^2/2}dz=0$.

The easiest way is to note that the integrand is an odd function.