Answer the following questions:

a. let x and y be independent normal random variables, each with mean μ and standard deviation σ. consider the random quantities x + y and x − y . find the moment generating function of x + y and the moment generating function of x − y .

b. refer to part (b). find now the joint moment generating function of (x + y, x − y ).

c. are x + y and x − y independent? explain your answer using moment generating functions.