Consider the conditional variance of X given Y. While none of the descriptions below are perfect, select the one that comes closest to giving a correct interpretation of Var(X|Y). O a. We imagine a two-step experiment, where we need to predict the value of X using the covariance of X and Y given an intermediate observation y (which we do not yet know) of Y. Then, Var( X|Y) will quantify the uncertainty of our prediction. O b. We imagine we are given i.i.d. observations (x, y) sampled from the joint distribution of X and Y. Then, Var(X|Y ) will quantify how much X will deviate from the straight line X = Y in the scatter plot. O c. Taking the expectation of Var(X|Y) with respect to the marginal distribution of Y tells us how much variation there is in X. In this sense, Var(X|Y) make up the contributions of variance in X that need to be summed up or integrated up (depending on whether Y is discrete or continuous) to find the marginal variance of X. O d. We imagine a two-step experiment, where we will be given some observed value y (which we do not yet know) of Y and, on the basis of this value, need to predict the variation of X in the sub-population that has Y = y: the prescription of how we will compute our answer is Var(X|Y). O e. Var( X|Y) is a measure of how much X will deviate from Y given a (future, not yet known) observed value y of Y