6. The distribution of the weight of a prepackaged "1-kilo pack" of cheddar cheese is assumed to be N(1.18, 0.072), and the distribution of the weight of a prepackaged *3-kilo pack" of cheese (special for cheese lovers) is N(3.22, 0.09²).
Select at random three 1-kilo packs of cheese, independently, with weights being X1, X2 and X3 respectively. Also randomly select one 3-kilo pack of cheese with weight being W. Let Y = X1 + X2 + X3.
(a) Find the mgf of Y
(b) Find the distribution of Y, the total weight of the three 1-kilo packs of cheese selected.
(c) Find the probability P(Y
