Let X; be independent Uniform(-6,6) random variables, for i=1, 2, ., 14. Let Y = X1+X2+...+X14 - (b) Find which of the following statements are correct for the moment generating function (mgf) My{t) of Y. O Itis equal to the sum of the mgfs of the Xi, for i=1,..,14 O Itis equal to the mgf of any Xi to the power of 1/14, for i=1,.,14 O The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. O Itis equal to 6 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14 O Itis equal to 14 times the mgf of Xi, for some integer i between 1 and 14 O Itis equal to the product of the mgfs of the Xi, for i=1,.,14 Give the following answers to three decimal places, where appropriate. (c) Find the expected value of Y. (d) Find the variance of Y.

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