Using a shuffled standard deck of 52 playing cards, a magician wants to do a trick where he tries to guess which card an audience member has selected if the audience member chooses a card at random and doesn't show the magician. Let X be the number of cards the magician will guess correctly if he tries the trick with 6 audience members. Each audience member starts with a complete and well-shuffled deck. The magician decides to call a trial a success if he guesses the number on the card correctly even if he doesn't get the right suit.
a. What are the possible values of X?
b. What is the mass of X?
c. Make a plot of the probability mass function.
d. What is the CDF of X?
e. Make a plot of the CDF.