The joint probability density function of random variables X1 , X2 and X3 is given by

The joint probability density function of random variables -VI , X 2 , andX3 is given by for > (0, 0, 0); o, (a) Determine the constant c . (b) Define the random variables Yl , Y2 , and Y; as Yl=Xl+X2+X3 Ys=xs (c) Find the marginal PDF of Yl , elsewhere. Find the joint PDF of VI , y; , and Y; , , as well as the bounds of y; , h , and Ys (i.e., the feasible domain of Yl , Y2 , and Y; ). Check that the "volume" under this joint PDF is equal to one.