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# System prepended metadata

title: Oral exam for Ellen

---

## Oral exam for Ellen


$$
 \frac{d}{dt} \langle x(t) \rangle =a + b  \langle x(t) \rangle
$$

$$
  \frac{d}{dt} \langle x(t)^n \rangle = ?
$$

$$
  \frac{d}{dt}\langle x(t)^n \rangle  + \mbox{terms involving }\langle x(t)^n \rangle = \mbox{other terms}
$$
$\to$ this is a diff eq. for $\langle x(t)^n \rangle$


variance
$$
\langle x(t)^2 \rangle_c = \langle x(t)^2 \rangle - \langle x(t) \rangle^2
$$

$$
  \frac{d}{dt} \langle x(t)^2 \rangle_c 
  =  \frac{d}{dt} \left(  \langle x(t)^2 \rangle - \langle x(t) \rangle^2\right)= ?
$$

last term:
$$
  2\langle x(t) \rangle ( a+b\langle x(t) \rangle )
$$