This question asks to show intermediate steps. The rest is for labeling and defining things so that we know what they are, making clear what probabilities you are calculating and labeling them as such (are they conditional, total, etc..? ) and providing your final number.

Let X be a random variable with density function: (,)= 2, 0 1

(a) How would you find the marginal pdf of X and the marginal pdf of Y.

(b) How would you find the ()E(X) and (2)E(X2) and calculate the variance of X.

(c) How would you find the conditional density function of x given y and the corresponding conditional expectation when y=0.3