Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density f(x, y) = {?2 +??/3 ,0 < ? < 1, 0 < ? < 2, 0 elsewhere. a. Verify if it is a valid density function. b. Find P[(X, Y) ∈ A], where A = {(x, y) | 0 < x < ½, ¼ < y < ½. c. Find the marginal density g(x).

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