Suppose that an urn contains 4 balls 1,3,5,8. We choose two balls at random from the urn without replacement.
Let X be the number on the first ball chosen and let Y represent the larger of the numbers appearing on the two
balls.
(a) State the joint pmf for the random vector (X; Y )
(b) Give the marginal distribution of X and the marginal distribution of Y .
(c) Find the expected value of X and the expected value of Y - X.
(d) Give the covariance of X and Y

Question

Suppose that an urn contains 4 balls 1,3,5,8. We choose two balls at random from the urn without replacement.
Let X be the number on the first ball chosen and let Y represent the larger of the numbers appearing on the two
balls.
(a) State the joint pmf for the random vector (X; Y )
(b) Give the marginal distribution of X and the marginal distribution of Y .
(c) Find the expected value of X and the expected value of Y - X.
(d) Give the covariance of X and Y