PROBLEM 1. Pick a point according to the uniform distribution from the interior of the triangle (in the R2 plane) with vertices (0,0), (1, 1), and (3, 2). (a). Find the density f(x) of the x-coordinate X of the random point. (Problem 4.1.12 is similar. The density is proportional to the length of the vertical cross- section.) (b). Find E(X). (c). Find the density g(y) of the y-coordinate of the random point. PROBLEM 1. Pick a point according to the uniform distribution from the interior of the triangle (in the R2 plane) with vertices (0,0), (1, 1), and (3, 2). (a). Find the density f(x) of the x-coordinate X of the random point. (Problem 4.1.12 is similar. The density is proportional to the length of the vertical cross- section.) (b). Find E(X). (c). Find the density g(y) of the y-coordinate of the random point