Answer to Question #43286 in Statistics and Probability for sam

Question

At the fair, you pay $5 to toss a ring at a set of bottles. If you get a “ringer” on the small mouth bottle, you win $35. If you get a “ringer” on the medium bottle, you win $10. If you get a “ringer” on the large bottle, you get your $5 back (break even). If you miss, you are out the $5 you paid to play. Probability of getting a ringer on the small, medium, and large bottles is 10%, 10%, and 5%, respectively. The probability distribution of Joe’s winnings (accounting for the $5 that he paid to play) in a single game is.

X -$5 $0 $10 $35
P 0.75 0.10 0.10 0.05

a. Find the math expectation of Joe’s winnings for a single game.

b. Find the math expectation of Joe’s winnings after 5 games.

c. Find the variance of Joe’s winnings for a single game.

d. Find the standard deviation of Joe’s winnings for a single game.

e. Does it pay for Ryan to play this game at the fair

f. Find the cumulative distribution function of Joe’s winnings for a single game and draw function