3. Let X and Y have the joint distribution Y\\X'-1 1 2 2 0.10 0.35 0.20 3 0.05 0.20 0.10 i.e. P(Y = 2 and X = 1) = 0.10. (a) Find the conditional distribution of Y given X : 32', and compute the mean of this distribution E[Y|X : .713], for ac : 1,1,2. (b) Is it true for this distribution that E [YlX : cc] is a linear function of :13? (0) Compute E[Y] from the distribution of Y, and compute E[Y] as a function of E[Y|X : :5] using the law of iterated expectations. ((1) Find the conditional variance of Y given X : 17 is. the variance of the conditional distribution of Y given X : l (which we may write formally as V[YlX : l] : E[(Y 7 E[Y|X : 1])2|X : 1] ). (e) If we write the joint distribution of X and Y as Y : E[Y|X] + 5, What is the conditional distribution of a given X = 1? (f) The 5 in Y : E[YlX] + 5 is called homoskedastic if V[lX : as] does not depend on 3:, and heteroskedastic otherwise. Describe in words What homoskedasticity means for the conditional distribution of Y given different values of X = 51:. Is 5 here homoskedastic or heteroskedastic