This question (Chapter 2 Problem 21) is from Bayesian Data Analysis, 3rd edition, by Gelman et al. It is a problem about a joint distribution from auto-regressive time-series model, y 1 ,y 2 ,....with mean level 0, auto-correlation 0.8, residual standard deviation 1. The normal errors can be written as (y t | y t-1 , y t-2 , ...) ~ N(0.8*y t-1 , 1) for all t . Q. what is the distribution of y t given y t-1 and y t+1 ? (i.e., given the observation 'before' and ;after' y t )