g Suppose that a temperature is represented by the random variable X, whose units are in Rankine, with standard deviation 6 Rank
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Answer:
Expected value = $8.89
Step-by-step explanation:
cost of playing game = $1
winning if sum is odd = $10
winning if sum is 4 or 8 = $5
winning if sum is 2 or 12 = $50
two dice rolled, possible outcomes =
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
total no. of outcomes = 36
now according to the table of outcome with respect to winning money, we can calculate expected value by multiplying the probability of each roll with winning amount associated with each roll. and subtract the amount that we paid for the game that is $1.
E(x) = 1/36*($50) + 1/18*($10) + 1/12*($5) + 1/9*($10) + 5/36*($0) + 1/6*($10) + 5/36*($5) + 1/9*($10) + 1/12*($0) + 1/18*($10) + 1/36*($50)
= 25/18 + 5/9 + 5/12 + 10/9 + 0 + 5/3 + 25/36 + 10/9 + 0 + 5/9 + 25/18
Expected value = $8.89
Subtract the amount that was paid to play the game that is $1.
$8.89 - $1 = $7.89
A profit of $7.89 is expected every-time the game is played.
