1. Suppose random variables X and Y appear together in the following way: X2021 0 Y 4-2 24-1 Assume that each observation is equally likely. (a) Find the joint probability mass function, fx,y. (b) Find the marginal probability mass function, the distribution function, and the expectation of Y. (c) Find the conditional expectation of Y given X = x, for each value of x. (d) Find the conditional expectation of Y given X. Find the expectation of the conditional expectation (i.e., E [ELYIX]]), and verity that it equals the unconditional expectation of Y (i.e., E[Y]).