Suppose random variables x and y are independent, and the moment generating function (mgf) of x is m_x = (4/5 e^t + 1/5)^9 and the mgf of y is m_y(t) = exp(3e^t - 3). a) use the mgt derivative approach to find the expectation and variance of x and of y. b) for each of the two variables x and y, based on the form of the respective mgt, determine the marginal distribution of the variable (the name with the value(s) of parameter( and without taking any derivatives find the expectation and variance of the variable. provide details. c) find p(2x + y = 4). d) find p(xy = 0). e) find e(xy).