first order auto regressive

Question

Hello how to do the following:

Suppose that $X =(X_1,X_2,...,X_n)$ follows the following:

$X_t - \mu = \eta (X_{t-1} - \mu) + \epsilon_t,$ $t= 1,2,...$

where $\mu \in R$ and $\eta \in (-1,1)$ unknown and $\epsilon_t$'s are iid from $N(0,1)$. Let $\theta = (\mu,\eta)$. Suppose $X_0 = 0$

What is the joint density function of $(X_1,X_2,X_3,..,X_n)$?

What is the maximum likelihood estimator for $(\mu,\eta)$?

Thanks a lot!