a. The random variables X and Y are such that their moment generating functions (MGFs) exist and are denoted as Mx(t) and My(t), respectively. Additionally, X and Y are independent random variables. Let Z = X + Y. Show that C. Mz(t) = Mx (t) My(t) One must decide whether X or Y are discrete or continuous RVs (your choice). It is suggested to use the definition of moment generating functions, the definition of expected values, and independence to show that the statement is true. If you don't use independence somewhere in your work, then most likely, you have an error. The random variables X is such that its mean and variance exists. Let Z = a + bX. Show that Var (Z) = b²Var (X) One must decide whether X or Y are discrete or continuous RVs (your choice) and use the definition of variance and expected values.

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