4. (20 points) A random variable is deﬁned to be Z = X +Y where X and Y are independent and both U ( −1 , 1). (a) Find the PDF of Z. (b) Use the PDF in part (a) to ﬁnd the mean and variance of Z. Note that whilte there are other ways of ﬁnding these values, you will only receive credit for using the PDF of Z.