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Course: High school statistics?>?Unit 7
Lesson 4: Expected value- Mean (expected value) of a discrete random variable
- Mean (expected value) of a discrete random variable
- Interpreting expected value
- Interpret expected value
- Expected payoff example: lottery ticket
- Expected payoff example: protection plan
- Find expected payoffs
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Find expected payoffs
Problem
An insurance company offers flood insurance to customers in a certain area. Suppose they charge for a given plan. Based on historical data, there is a probability that a customer with this plan suffers a flood, and in those cases, the average payout from the insurance company to the customer was .
Here is a table that summarizes the possible outcomes from the company's perspective:
Event | Payout | Net gain |
---|---|---|
Flood | ||
No flood |
Let represent the company's net gain from one of these plans.
Calculate the expected net gain .