Expected Value of Probability Distribution Function

Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6

• 14

• 4.67

• 5

• 7.5

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

• 1.75

• 1.84

• 2.00

• 2.50

The table shows the probability distribution of a fair six-sided die. Determine 𝐸(𝑋).

give your answer to 1 decimal place.

The function in the given table is a probability function of a discrete random variable 𝑋. Given that the expected value of 𝑋 is 6.5, find the value of A.

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

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

• $1

• $0.50

• -$0.50

• $0

In a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. If a household is selected at random, what is the expected number of children in that household? HINT: A Probability table may be helpful.

• 2.00

• 2.13

• 1.97

• 1.27

A fair, 6-sided dice is thrown 120 times.

Roughly how many times would you expect the number 5 to come up?

• 6

• 10

• 12

• 20

Sam’s pencil case contains 3 red, 2 blue and 5 black pens. He takes a pen out without looking then puts it back 500 times. Roughly how many times would you expect him to pick up a blue pen?

• 50

• 100

• 200

You roll a standard die. You win $12 if you roll a six, $6 if you roll a one, and $0 if you roll anything else. What is the expected value of a single roll?

• $3

• $18

• $9

• $2