Finding Expected Values of Random Variables

Given the probability model in the table below, what is the expected value of the random variable?

X 40 20 5

P(X) 0.15 0.3 0.55

• 14.75

• 5

• 3.75

• 7.5

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

• yes

• no

Eva flips a coin. If she gets heads, she wins $3. If she gets tails, she loses $4. What is her expected value of a coin flip?

• $1

• $0.50

• -$0.50

• $0

Find the mean (expected value) of the probability distribution.

• 85

• 83.2

• 87.1

• 84.4

Suppose you buy a ticket for $8 out of a lottery of 1000 tickets where the prize for the one winning is to be $800. How much money do you take home (after paying for it)?

• $800

• -$6.50

• -$6

• -$7.20

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. Is this a fair game?

• yes

• no

A student group sells 500 raffle tickets for $2 each. At the drawing the top prize will be a gift certificate for $100. Second prize will be a $50 gift card and there will be five 3rd prizes, each a $20 gift card. Do you expect to win or lose (on average)? How much?

• lose an average of $5.50

• lose an average of $1.50

• win an average of $2.00

• lose an average of $10.00

Find the expected value, round to 3 decimal places.

• 0.4

• 0.6

• 0

• 1.1

Calculate the missing outcome

• 8

• 10

• 12

• 15

Choose an American household at random. What is the expected number of cars for that household?

• 1.75
• 1.84
• 2.00
• 2.50