1 Find the expected value of the random variable.ġ0 Example 1 continued…. The expected value of a (discrete) random variable can be found by summing the products of each possible value by the probability that it occurs: Note: Be sure that every possible outcome is included in the sum and verify that you have a valid probability model to start with. Who wants to play? Would you play for a top prize of $200? For any other ace, I will pay you $10, and for any other heart, I will pay you $5. If you draw the ace of hearts, I will pay you $100. What strategy were you using? (There is an optimal strategy.)ħ Let’s Play a Game!! A player will pay me $5 and then draw a card from a deck. BUT…if I roll a 5, all those still standing lose their points, ending the round with a score of 0. With each roll, points accumulate for those who choose to remain standing. Students then may choose to keep their points by sitting down, or remain standing for another roll. Each student will get the number of points on the die. Of particular interest is the value we expect a random variable to take on, notated μ (for population mean) or E(X) for expected value.Ħ Greedy Pig All students stand up. Example: Cost of books this termĪ probability model for a random variable consists of: The collection of all possible values of a random variable, and the probabilities that the values occur.
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Example: Number of credit hours Continuous random variables can take any numeric value within a range of values.
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There are two types of random variables: Discrete random variables can take one of a finite number of distinct outcomes. A particular value of a random variable will be denoted with a lower case letter, in this case x. We use a capital letter, like X, to denote a random variable. Publishing as Pearson Addison-WesleyĪ random variable assumes a value based on the outcome of a random event. Presentation on theme: "Chapter 16 Random Variables"- Presentation transcript:Ĭopyright © 2007 Pearson Education, Inc.