Question

A game similar to The Wheel of Fortune is played by turning a fair wheel with 16 equal sectors labeled with numbers from 1 to 16. Each game consists of only one (1) run by turning the wheel. For each game, player wins $1200 if the needle lands on the number 1 when the wheel stops turning. Similarly, player wins $375 if the needle lands on any of the numbers 2 to 4, $170 if the needle lands on any of the numbers 5 to 8, and $60 if the needle lands on any of the numbers 9 to 14. Player wins nothing (winning $0) if the needle lands on the number 15, and gets a bankruptcy (losing $-3300) if the needle lands on the number 16. Suppose the fee is $5 to play each game. Let the random variable XX be the winning/losing amount received from this game.

A) In the table below, complete the probability distribution of XX. Leave your answer in fractions.

Table looks like this:

XX	P(X)P(X)

B) Compute the expected value of XX, E(X)E(X), from this probability distribution. Round your answer to two decimal places.
E(X)=

THIS IS A STATS PROBLEM AND I WAS UNABLE TO SOLVE IT. please solve it.

Answer 1

Let X: winning amount received from the game.

A wheel has 16 equal sectors. Each sector has an equal probability like 1/16.

The fee of the game is $5.

If the wheel stops on number 1 player win $1200, so the actual amount in hand to the player is 1200 - 5 = 1195 ($5 is the fee of the game so it will be subtracted from each winning amount) with the probability of 1/16

If the wheel stops on numbers 2 to 4 that is either 2, 3 or 4 player wins $375 that is 375 - 5 = 370 and the probability is 3/16

If the wheel stops on numbers 5 to 8 that is either 5, 6, 7 or 8 and player wins $170 that is 170-5 = 165 and the probability is 4/16 (that is 1/16 + 1/16 + 1/16 + 1/16)

If wheel stops on numbers 9 to 14 that is either 9, 10, 11, 12, 13, or 14 then player wins $60 that is 60-5 = 55 and the probability is 6/16 since there are 6 numbers.

If the wheel stops on number 15 then player wins nothing that is 0 means 0 - 5 = -5 and the probability is 1/16

If the wheel stops on number 16 then player losses -3300 that means actually -3300 - 5 with probability 1/16  

A. Probability distribution table:

X	P(X)
1195
370
165
55
-5
-3305

B. Expected value:

The formula of expected value,

Expected value = 1195 * (1/16) + 370 * (3/16) + 165 * (4/16) + 55 * (6/16) + (-5) * (1/16) + (-3305) * (1/16) = -0.9375

Expected value = -0.94

Negative expected value represents loss.