Let X denote an unknown quantity that has three possible values: 2, 3, and 7, and suppose that their probabilities are P(X = 2) = 0.260, P(X = 3) = 0.675, P(X = 7) = XXXXXXXXXXLet Y denote another...

Let X denote an unknown quantity that has three possible values: 2, 3, and 7, and suppose that their probabilities are P(X = 2) = 0.260, P(X = 3) = 0.675, P(X = 7) = 0.065. Let Y denote another unknown quantity that has three possible values: −1, 3, and 4, and suppose that their probabilities are P(Y = −1) = 0.065, P(Y = 3) = 0.675, P(Y = 4) = 0.260. (a) Compute E(X), Stdev(X), E(Y), and Stdev(Y). (b) According to the Central Limit Theorem, an average of 36 random variables drawn from the probability distribution of X should have approximately what probability distribution? (Be sure to specify the mean and standard deviation.) (c) In a spreadsheet, make a simulation table that tabulates values of five random variables as follows: The first is a single cell that simulates X. The second is a single cell that simulates Y. The third is an average of 36 cells independently drawn from the probability distribution of X. The fourth is an average of 36 cells independently drawn from the probability distribution of Y. The fifth is a single random cell drawn from the probability distribution that you predicted in (b). Include at least 400 data rows in your simulation table. (This calculation may take a few minutes on older computers.) (d) Using your simulation table in (c), compute the sample mean and standard deviation for each of the five random variables and make an XY chart that estimates the (inverse) cumulative distribution for these five random variables. (Hint on charting keystrokes: You can separately sort each of your five columns of simulation data, then select the percentile index and five sorted data columns in the simulation table and insert an XY chart.)