- #1

andresthor

- 3

- 0

## Homework Statement

I'm trying to find the expected value of a probability distribution.

## Homework Equations

[tex]\int_{-\infty}^\infty xP(x,t) = \int_{-\infty}^\infty x \frac{1}{\sqrt{4\pi Dt}}e^{-\frac{(x-dt)^2}{4Dt}}dx[/tex]

## The Attempt at a Solution

I expect the value to be something like $dt$ but then again I might be way off.

I've tried some different substitutions but have had no luck. One example of what I've been trying:

[tex]

\begin{equation}

\frac{1}{\sqrt{4\pi Dt}}\int_{-\infty}^\infty x e^{-\frac{(x-dt)^2}{4Dt}}dx=\left/ u=x-dt\right/ = \frac{1}{\sqrt{4\pi Dt}}\int_{-\infty}^\infty (u+dt) e^{-\frac{u^2}{4Dt}}du = \frac{1}{\sqrt{4\pi Dt}}\left(\int_{-\infty}^\infty u e^{-\frac{u^2}{4Dt}}du + dt \int_{-\infty}^\infty e^{-\frac{u^2}{4Dt}}du\right)

\end{equation}

[/tex]

But then I get nowhere.