3. (Exercise 1 on p. 295 of MMSA revised) A particular brand of dishwasher soap is sold in 3 sizes: 25 oz, 40 oz, and 65 oz. The percentage of all purchasers that select a 25-02 box, 40-02 box, and 65-02 box are respectively, 20%, 50%, and 30%. Let X1 and X2 denote the package sizes selected by two independently selected purchasers. (a) What is the pmf of X1? Find u = E(X1) and 02 = Var(X1). (b) The follow table lists all possible values (331, 2) for the pair (X 1, X2) and the corresponding prob- ability p(X1 = x1,X2 = :02) and the mean X = (X1 + X2)/2 for each pair. Please complete the table. 331 25 25 25 40 40 40 65 65 65 1' 2 25 40 65 25 40 65 25 40 65 P(X1=331,X2=L'2) f: (X1+X2)/2 0.2 x 0.2 = 0.04 (25 + 25) /2 = 25 0.2 x 0.5 = 0.10 (25 + 40) /2 = 32.5 and use the table above to nd the sampling distribution (i.e., pmf) for Y. Hint: See Example 6.2 on 10288-290 of MMSA