Random Variable Expected Value

A game involves rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of green wins $2.00. A roll of blue wins $5.00.  The charge to play the game is $2.00. What is the expected value

• $0

• -$0.50

• $.67

• $-1.50

If the expected value is positive, are you expected to win?

• yes

• no

Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 4 or a 2, and nothing otherwise.  What is the expected amount you win?

• $0.00

• -$1.00

• $1.00

• $3.00

A stockbroker estimates that at the end of the year, there is a 40% chance a stock will be worth $50, a 35% chance it will be worth $60 and a 25% chance it will be worth $70.
What expected value does this broker assign to this stock's end-of-the-year price?

• $58.50

• $60.00

• $62.50

• $65.00

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

The table above shows a television station's advertisement sales. The distribution of sales for one 24-hour day is given. Solve for the mean. Round to the nearest hundredth.

• 31.8

• 15.68

• 0.20

• 1.00

A car dealer buys hybrids for $21,000 each and sells them for $24,500 each. Find his expected weekly profit.

• $2,380

• $5,355

• $8,109

• $37,485

A coin is flipped 3 times. If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?

• $12.50

• $5

• $7.50

• $10