A player selects two cards at random without replacement from an ordinary deck of 52 cards.
Let random variables X and Y denote the number exposed on the first and second cards, where jack, queen and king are counted as 11, 12 and 13, respectively.
(a) Find the conditional PMF of Y given X = x, where x ∈ {1, 2, . . . , 13}.
(b) Find the joint PMF of X and Y .(c) Find the mean and standard deviation of X and Y .
(d) Find ρ(X, Y ), the correlation coefficient of X and Y . Provide a brief intuitiveexplanation for the negative sign of your answer.
