An (incomplete) card deck contains 36 cards, of ranks 2, 3, 4, 5, 6, 7, 8, 9, 10 (of all four suits). Two cards are picked at random without replacement. Let Z denote the random variable which is the maximal rank of the two cards picked (for example, if 6, 7 are picked then Z = 7).
Compute the probability mass function and the cumulative distribution function of Z.
PMF = P(X=x)= ????
What is the expected value (i.e. math. expectation) of Z?
I have been reading about the concept of probability mass functions for 20 minutes and I cannot really understand how it is applied to this problem... I understand that it deals with discrete random variables which is obviously relevant to this problem.