In the Chinese version, fair dice with numbers 1, 2, 3, 4, 5, and 6 are used, along with a board with those numbers. The board has those six objects on it, also. We will play with bets being $1. The player places a bet on a number. The "house" rolls three dice. If none of the dice show the number that was bet, the house keeps the $1 bet. If one of the dice shows the number bet (and the other two do not show it), the player gets back his or her $1 bet, plus $1 profit. If two of the dice show the number bet (and the third die does not show it), the player gets back his or her $1 bet, plus $2 profit. If all three dice show the number bet, the player gets back his or her $1 bet, plus $3 profit.

Complete Question:

a) List the values that y may take on and construct the pdf table

b) Calculate the average expected matches over the long run of playing this game for the player

c) Calculate the average expected earnings over the long run of playing this game for the player

a) Y = { -1, 1, 2,3}

E(X) = 0.5

c) There is a loss of $0.0802

Explanation:

a) Y will take on the values, Y = { -1, 1, 2,3}

The pdf table is attached as a file to this solution

b) E(X) = 0.5

c)

The average expected matches, E(X) = np

where p = 1/6, n =3

E(X) = 3 * 1/6

E(X) = 0.5

c) Average expected earnings =

P(y) can be seen from the pdf table in the file attached

Average expected earning = (-1*0.579) + (1*0.347) + (2*0.069) + (3 * 0.0046)

Average expected earning = -0.0802

This shows that instead of earning, there is a loss of $0.0802

answer; and he had to live thus all alone on the brink of an abyss, with no one who understood or pitied him;