Let X denote an unknown discrete 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 discrete 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.

Question (1). Compute E(X), Stdev(X), E(Y), and Stdev(Y). (3 points)

Question (2). 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.) (4 points)

Question (3). In a spreadsheet, make a simulation table that tabulates values of five random

variables as follows: (5 points)

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 (2).

Include at least 400 data rows in your simulation table.