Question are listed below

Exercise 4 (2+2+2+1+1+1+1 pts). Uniform continuous random variables. Suppose Smokey the Bear is camping on the Olympic peninsula and a y gets trapped in his tent. Let the tent be represented by the polyhedron P with vertices (0, O, O), (0, 1, O), (1, 1, O), (1, O, O), (0, 1/2, 1), (1, 1/2, 1) and let the position of the y be represented by the random vector (X, Y, Z). Assume that the position of the y is uniformly randomly distributed within P. 1. Compute the marginal p.d.f. of X 2. Compute the marginal p.d.f. of Y 3. Compute the marginal p.d.f. of Z