A box contains 12 marbles. Six of the marbles are red, four are green, and two are yellow. Suppose that you choose three marbles at random. let x be the number of red marbles in the sample, y be the number of green marbles, and z be the number of yellow marbles. a. Give the precise formulas for the probability mass functions of the three random variables, f(x), f(y), and f(z). b. Suppose you win $1 for each green marble in your sample and lose $1 for each red marble (yellow has no financial consequences). Let w be your net winnings or losses. Construct the P.M.F of w as a table. (obviously the table part cannot be shown in this answer) c. Find the expected value of w and explain its significance. d. Find the standard deviation of w. Any help is greatly appreciated! If anyone can point me in the right direction, that'll be great!