Just Solve for 3-193. 3-171 is just a reference.

3-171. A grocery store tracks the joint distribution of the number of apples and oranges in each customer transaction (with some rounding). Let X and Y denote the number of ap- ples and oranges, respectively, and assume the following joint distributionX 6 12 0.5 0.05 0.1 Nao 0.05 0. 1 0.05 0. 1 0.05 0 Determine the following: (a) P(X = 6, Y = 6) (b) P(X 6) (d) P(X = 6) (e) P( X = 6) (f) Whether or not X and Y are independent3-193. Consider the random variables in Exercise 3-171. Determine the following: (a) E (2X + Y) (b) Cov (X, Y) (c) V( X + 3Y) (d) PXY