3. Let Z1, ..., ZN be a sequence of independent Gaussian random variables with mean 0 and variance 1. You observe the random vector X in R^ that is generated through the autoregressive process Z1, k =1 XK = aXk-1+ Zk, k > 1. Given X = x, find the MLE for a E R. (Hint: Conditional independence.) (Further hint: The conditional independence structure makes this a Markov process, meaning that we can factor the distribution for X ER as fx (a) = fx, (x1) fx2(2|1) fx3(203|202) . . . fXN (2N |2N-1)