A magician wants to do a trick where he tries to guess the value of the card that an audience member has selected (the suit of the card is not taken into account). He has six decks of cards so he gives one deck to each of six audience members. Let X denote the number of cards that he guesses correctly, when each audience member selects one card at random.
a. Find E(X).
b. Find E(X2).
c. Find Var(X).
d. The magician gets paid $500 for performing the show, plus $20 for each card he guesses correctly. What is the average amount of money that he gets paid?
e. As in (d), what is the variance of the amount that he gets paid?