Applicants for the University of Statland take two tests, one for writing ability and the other on critical thinking, and normalized scores are recorded on each between 0 and 1. For a given applicant, let X be the score on the writing test and YY the score on the critical thinking test. A model for the joint probability density function for the two test scores can be taken as:

f(x, y) = { x+y for 0 < x < 1, 0 < y < 1

{ 0 elsewhere.

(a) Find the marginal density of the writing test score, and evaluate it at the point X = 1/2.

(b) Find the marginal density of the critical thinking test score, and evaluate it at the point Y = 1/3.