This question (Chapter 3 Problem 15) is from Bayesian Data Analysis, 3rd edition, by Gelman et al. It is a problem about a joint distribution from...

This question (Chapter 3 Problem 15) 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, y1,y2,....with mean level 0, auto-correlation 0.8, residual standard deviation 1. The normal errors can be written as (yt | yt-1, yt-2, ...) ~ N(0.8*yt-1, 1) for all t.

Q. what is the distribution of yt given yt-1 and yt+1? (i.e., given the observation 'before' and ;after' yt) ?