Two cards drawn at random from a pack of cards with replacement. let the random variable x be the number of card drawn from the heart suit.
a. construct a probability mass function
b. construct a cumulative distribution function
c. what is the most likely value of the random variable x?

This is a discrete distribution with three possible cases of interest. In any such two-card hand, you can have (1) no cards, (2) one card, or (3) both cards with the heart suit.



As a PMF, you would say



The CDF is given by



The most likely value of is the expected value for the distribution, which is given by