2 Continuous Intro (3) Is 2x, 03x31 x : ) {0, otherwise a valid density function? Why or why not? Is it a valid CDF? Why or why not? (b) Calculate IE[X] and Var(X) for X with the density function 1/6, 0 S x S E, f(x) {0, otherwise. (c) Suppose X and Y are independent and have densities 2x, 0 S x g 1, fx (3') = . 0, otherw15e, 1, 0 g y g 1, 0, otherwise. 1310'): { What is their joint distribution? (Hint: for this part and the next, we can use independence in much the same way that we did in discrete probability) ((1) Calculate IE[X Y] for the above X and Y