Four balls are randomly placed, one at a time, into four urns (so that it is possible for more than one ball to be in any particular urn). Let the random variable X be the number of urns that are occupied. Let the random variable Y be the number of balls in the first urn.
(a) What type of distribution is Y, with what parameter or parameters?
(b) What is the value of E[Y] ?
(c) For each possible value of Y, beginning with the hightest (Y = 4), determine the probability mass function for the conditional probability P(X|Y).
(d) Are X and Y independent? Why or why not?