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 (0,0, 0), (0, 1,0), (1, 1,0), (1,0, 0), (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. 2. Image-0o Compute the marginal p.d.f. of X Compute the marginal p.d.f. of Y . Compute the marginal p.d.f. of Z Are X, Y, Z independent? . Are X and Y independent? . Are X and Z independent? . Are Y and Z independent