6. Suppose we select one point at random from within the circle with radius R. If we let the center of the circle denote the origin and define X and Y to be the coordinates of the point chosen in this circle, then (X, Y) is a uniform bivariate RV with joint PDF given by f(x, y) [k, x² + y² ≤ R² otherwise 0, - {6 where k is a constant. (a) Determine the value of k. (b) Find the marginal PDF's of X and Y. (c) Find the probability that the distance from the origin of the point selected is not greater than a.

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