the question is below picture.

We have two random quantities X and Y. Marginally Y has a standard normal distribution Y ~ N(0, 1). Conditional on Y = y, X has a normal distribution (X Y = y) ~N (by, v) for known fixed numbers b, v > 0. (a) What are EX and Var X ? (Hint: use the law of total expectation and the law of total variance. (b) Derive the conditional distribution of Y |X = x. (c) Assume b = 0.8 and v = 1. Suppose we observe X = 5, what is posterior mean of (Y X = 5)? What do you expect the posterior mean of Y to change when the value of X increases