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