You want to set up a games stall at the Winter Wonderland. You have a single pack of 52
cards and decide to play card games with your customers. The game is designed as follows. A
customer draws 4 cards at random. For every “Ace” that the customer draws, he/she wins £3
and for every face card (“Jack”, “Queen” or “King”), he/she wins £1.
Let the two discrete random variables U and V, be the number of aces and face cards
obtained, respectively.
(i) Derive the joint probability mass function p(U, V).
(ii) Find the marginal probability mass functions of U and V.
(iii) Are U and V independent? Specify the reason.
(iv) Find E(U), E(V), Var(U), Var(V) and Cov(U, V) and interpret the obtained values.
(v) Find the minimum price for the game, so that you don’t bear a loss if a very large
number of games are played.
(vi) If you set the price for each game by rounding up the value found in (v), find the
percentage of people who will go back home with positive winnings.
1 answer
1 answer