Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate.

4. Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (21) (Spts). If X N EmpUQ with )\\ > 0, and Y = e'AX, then Y is uniformly distributed on [0, 1]. (b) (Spts). If X1 has density function f1 and X2 has density function f2, then X1 + X 2 has density function f1 + f2. 84\"\") .1; > 0,11; > 0, (c) (9pts). If the variables X and Y have joint density x, 3;) = _ 0 otherwme, then X and Y are uncorrelated