Let Xi be independent Uniform(−6,6) random variables, for i=1, 2, ..., 13.  Let Y = X1+X2+...+X13 .   (b) Find which of the following statements are correct for the moment generating function (mgf) MY(t) of Y.     A The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. B It is equal to the sum of the mgfs of the Xi, for i=1,...,13 C It is equal to the mgf of any Xi to the power of 1/13, for i=1,...,13 D It is equal to 6 times the mgf of any Xi to the power of 13, for some integer i between 1 and 13 E It is equal to 13 times the mgf of Xi, for some integer i between 1 and 13 F It is equal to the product of the mgfs of the Xi, for i=1,...,13  (c) Find the expected value of Y. (d) Find the variance of Y.

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