Imagine you are in a game show There are 4 prizes hidden on

Imagine you are in a game show. There are 4 prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and two are worth $10. You have to pay $20 to the host if your choice is not correct. Let the random variable x be the winning. Show all work. Just the answer, without supporting work, will receive no credit.

(a) What is your expected winning in this game? (5 pts)

(b) Determine the standard deviation of x. (Round the answer to two decimal places) (10 pts)

Solution

Let the spaces be 1,2....10

Each has equal prob = 0.1 Win amt x prob winamt^2 x prob

Of these 1 space has winning 100 10 1000

1 winning 50 5 250   

2 worth 10 2 20

7 worth -20 -14 280

a) Expected winning = sum of win amt x prob = 3

b) variance of winning = 280-3^2 =271

std dev = 16.46