a) If each player acts independently of the other, and if each player makes his choice of the number of fingers he will hold up and the number he will guess that his opponent will hold up in such a way that each of the 4 possibilities is equally likely. (b) Suppose that each player acts independently of the other. If each player decides to
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1. In the game of Two-Finger Morra, two players show 1 or 2 fingers and simultaneously
guess the number of fingers their opponent will show. If only one of the players guesses
correctly, he wins an amount (in dollars) equal to the sum of the fingers shown by him
and his opponent. If both players guess correctly or if neither guesses correctly, then no
money is exchanged. Consider a specified player, and denote by X the amount of money
he wins or loses in a single game of Two-Finger Morra. Find the pmf of X if
(a) If each player acts independently of the other, and if each player makes his choice of
the number of fingers he will hold up and the number he will guess that his opponent
will hold up in such a way that each of the 4 possibilities is equally likely.
(b) Suppose that each player acts independently of the other. If each player decides to
hold up the same number of fingers that he guesses his opponent will hold up, and
if each player is equally likely to hold up 1 or 2 fingers.
2. Determine the constant c so that f(x) satisfies the condition of being a pmf for a random
variable X
(a) f(x) = x/c, x = 1,2,3,4
(b) f(x) = c(1/5)x, x = 0,1,2
(c) f(x) = c(1/5)x, x = 1,2,3,...
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