For which one of the following situations would Kendall’s tau be appropriate? a) The Mohs scale rates the hardness of minerals. If one mineral can scratch another, it is judged….

## Find the marginal probability mass functions pX (x) and pY (y).

1. A penny and a nickel are tossed. The penny has probability 0.4 of coming up heads, and the nickel has probability 0.6 of coming up heads. Let X = 1 if the penny comes up heads, and let X = 0 if the penny comes up tails. Let Y = 1 if the nickel comes up heads, and let Y = 0 if the nickel comes up tails.

a. Find the probability mass function of X.

b. Find the probability mass function of Y.

c. Is it reasonable to assume that X and Y are independent? Why?

d. Find the joint probability mass function of X and Y.

2. Two fair dice are rolled. Let X represent the number on the first die, and let Y represent the number on the second die. Find µXY.

3. A box contains three cards, labeled 1, 2, and 3. Two cards are chosen at random, with the first card being replaced before the second card is drawn. Let X represent the number on the first card, and let Y represent the number on the second card.

a. Find the joint probability mass function of X and Y.

b. Find the marginal probability mass functions pX (x) and pY (y).

c. Find µX and µY .

d. Find µXY .

e. Find Cov(X,Y).