Imagine you are in a game show. There are 10 prizes hidden on a game board with

Question

Imagine you are in a game show. There are 10 prizes hidden on a game board with 100 spaces. One prize is worth $50, two are worth $20, and another seven are worth $10. You have to pay $5 to the host if your choice is not correct. Let the random variable x be the winning. a. Complete the following probability distribution. (Show the probability in fraction format and explain your work)

x

P(x)

-$5

$10

$20

$50

(b) (2 pts) What is your expected winning or loss in this game? Be specific in your answer whether it’s winning or loss. (Show work and round the answer to two decimal places)

(2 pts) What is the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)

x

P(x)

-$5

$10

$20

$50

Explanation / Answer

a)

There are 90 losing spaces, 7 with winning $10, 2 with winning $20, and 1 with winning $50. Hence, we divide these by 100 to get

*************************************

b)

Consider:

Thus,  
  
E(x) = Expected value = mean = Sum(xP(x)) =    -2.9

Hence, as it is negative, AN EXPECTED LOSS OF $2.90. [ANSWER]

*******************************

c)

Also,

Var(x) = E(x^2) - E(x)^2 =    54.09

Thus,

s(x) = sqrt [Var(x)] =    7.354590403 [ANSWER, STANDARD DEVIATION]

x P(x) -5 90/100 10 7/100 20 2/100 50 1/100

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.