Suppose that the random variables x, y, and z have the following joint probability distribution. xyz(x, y, z) 1 1 1 0.05 1 1 2 0.10 1 2 1 0.15 1 2 2 0.20 2 1 1 0.20 2 1 2 0.15 2 2 1 0.10 2 2 2 0.05 determine the following: a. p(x = 2) b. p(x = 1, y = 2) c. p(z < 1.5) d. p(x = 1 or z = 2) e. e(x) f. p(x = 1 | y = 1) g. p(x = 1, y = 1 | z = 2) h. p(x = 1 | y = 1, z = 2) i. conditional probability distribution of x given that y = 1 and z = 2