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# chapter10 - Chapter 10 The Expected Value and Standard...

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Chapter 10 The Expected Value and Standard Error This chapter introduces us to the very important concepts of random pro- cesses and their sampling distributions. To keep ideas manageable, it is best motivated by way of example. 10.1 Expected value Assume 100 draws are made randomly with replacement from a box con- taining 4 tickets labelled 1,1,1, and 5 as follows: 1 1 1 1 5 What would be the expected sum of the 100 draws? We can expect the ticket labelled 1 to be picked 75 times and the ticket labelled 5 to be picked 25 times on average. So the sum would be, on average, 1 × 75+5 × 25 = 200 . This average, of the sum of 100 draws, is known as the expected value . 1 This is the ﬁrst example in which we use what is called a box model. Note that this kinds of model will be used throughout the book. 1

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2 CHAPTER 10. THE EXPECTED VALUE AND STANDARD ERROR A quick way to get the expected value, usually denoted EV, for the sum of draws made at random with replacement from a box equals: EV = Average of box
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chapter10 - Chapter 10 The Expected Value and Standard...

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