1. Consider a man betting on a dice game at a casino. The “dealer” rolls the fai

Question

1. Consider a man betting on a dice game at a casino. The “dealer” rolls the fair die and gives the man $1 if it is a 5, $2 if it is a 6. The man gets $0 if it is a 3 or a 4. He loses $1 if it is a 2 and $2 if it is a 1.

a. Define a random variable X that is relevant to this problem (Hint: X should account for the man’s “winnings” when the die is rolled). List out the values that X can take. (1 point)

b. Write out the probability distribution table for X. (2 points)

c. What can the man expect to win in one roll of the die?

Explanation / Answer

A) HERE THE X WILL BE THE AMOUNT WINNINH OR LOSING.

VALUES FOR X = -2,-1,0,1,2

B) DISTRIBUTION   

X P(X)

-2 1/6

-1 1/6

0 1/3

1 1/6

2 1/6

C) EXPECTATION E(X) = X1*P(X1)+X2(PX2)+....XN*P(XN)

HERE -2*1/6 -1*1/6 +0*1/3 +1*1/6+2*1/6 = 0

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