Expected Value Worksheet

Expected Value Worksheet

Read each question carefully and answer to the best of your ability. Show all work for calculation problems.

1. What does the expected value of a random variable represent?

2. In a game, you win $10 if you roll a 6 on a standard six-sided die, and lose $2 otherwise. What is the expected value of playing this game once?

3. The formula for expected value E(X) is the sum of each outcome multiplied by its  .

4. If the expected value of a game is negative, it means that, on average, you can expect to   money over many plays.

5. A company is considering investing in a new project. There is a 40% chance of making a profit of $50,000, a 30% chance of breaking even, and a 30% chance of losing $20,000. Calculate the expected monetary value of this project.

6. The expected value must always be one of the possible outcomes of the random variable.

7. A carnival game involves spinning a wheel with 8 equally likely sections. Four sections award $0, three sections award $5, and one section awards $20. It costs $3 to play the game. Should you play this game? Justify your answer using expected value.

8. Consider a random variable X with the following probability distribution:

P(X=1) = 0.2

P(X=2) = 0.5

P(X=3) = 0.3

Represent the expected value of X on a number line.