1. Consider continuous random vector (X, Y) whereX ~ NU), 1) (standard normal) and Y|X = a: w N{:s, l) (the conditional distribution of Y given X = a: is normal with mean a: and variance 1). (a) Findthejointpdfof (X,Y). (b) Find the marginal distribution of Y. (c) Consider random vector (V, W} where W ~ N (Cl, 2} {normal with mean El and variance 2). How should the conditional distribution V|W = u: be chosen so that (V, W) has the same distribution as (X, Y}