Chapter 20

# Chapter 20 - Chapter 20 Expected Values Motivation Do you...

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Chapter 20 Expected Values

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Motivation Do you think the following probabilities are correct for payout on a 1\$ lottery ticket? Why/Why not? Money you win: 0\$ 1\$ 5\$ 100\$ Probability win: .8 .1 .05 .05 Suppose that you buy 1000 of the 1\$ lottery tickets w/ payouts above. How much money do you think you’ll make per ticket (on average). i.e. in the long run.
Outline Expected Values Law of Large Numbers Thinking About Expected Values: Inference and Variability Finding Expected Values via Simulation

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Expected Values
Definition Recall: A random variable is used to represent a set of possible outcomes of a random phenomenon numerically. Ex. If we flip a coin 5 times. The random variable X is could be the number of heads. What are possible values of the random variable? Ex. Suppose we count the number of children a couple has until they have a girl. What is the random variable? What are possible values it can take on?

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Random variable/phenomenon Random phenomenon Don’t know what will happen one time Do know what tends to happen in the long run Random Variable assigns outcomes or events of an experiment a number. Ex. X = number of heads in 2 coin flips What do you think the average outcome will be in terms of the random variable?
Definition The expected value of a random variable is defined as the average long run value of the random variable. Ex. Flip a coin twice.

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## This note was uploaded on 06/15/2011 for the course STAT 110 taught by Professor Johnson during the Fall '07 term at South Carolina.

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Chapter 20 - Chapter 20 Expected Values Motivation Do you...

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