options: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.

Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
problem_activity: Task
Bob’s Bagel Shop has estimated the following probabilities for the number of bagels a randomly-selected customer buys when he or she enters the shop.
| No. of Bagels | Probability |
|---------------|-------------|
|       1       |     .5      |
|       2       |     .1      |
|       3       |     .1      |
|       6       |     .1      |
|      12       |     .2      |
Bob sells bagels for \$0.80 each, or \$9.00 for a dozen. If $X =$ the amount of money Bob collects from a randomly-selected customer, find and interpret the expected value of $X$.


correct_option_index: 2