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ch10 - Ch 10 TheExpectedValueand StandardError Weneed...

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1 Ch 10 The Expected Value and  Standard Error Chance Processes    Recording the HEADS from tossing a coin •  The amount of daily gains from owning a share •  Recording the monthly unemployment rate   We need  to analyze  these as  chance  processes 100 Box Model  can  simplify complex  phenomenon.

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2 Sampling :    For example, sampling from a population of interest can be  understood using a box model Chance pr ocess Box model Box Ti cket Popul at i on pi cki ng Pi cked t i cket s sampl i n g σ μ , S X , Par amet er s, Sampl e Popul at i on
3 A closer look at the BOX MODEL This is repeated  10 times: totals  are … 88 84 80 90 83 78 95 94 80 89 The smallest sum should be 25 and largest 150 In our experiment  the sum was between  75  and  100 . • A ticket from the box are drawn  randomly. • The ticket is returned and then another  one is drawn randomly. • The numbers on the card are recorded. Box 2 3 4 6 5 Dr aw 25 dr aws ( wi t h r epl acement ) 1 32462 35442 36412 41556 22255 TOTAL : 88

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4 Using the BOX MODEL 2 3 4 6 5 1 25 Car ds Pi cked 1 2 3 4 5 6 What number s go i nt o t he box? 1 How many of each ki nd? 2 How many dr aws? 3
5 What number s? 1 The chance of dr awi ng any par t i cul ar number must be equal t o t he chance of wi nni ng/ l osi ng on a si ngl e pl ay. The number of dr aws equal s t he number of pl ays. We can now add t he t ot al . How many of each? 2 How many dr aws? 3 W i n/ l ose? 4 +1000 - 1000 EX) A die is thrown. You win Baht 1000 if an odd  number appears, you lose Baht 1000 if an even number  appears. How much do you expect to win or lose in 20  trials? - 1000 +1000 +1000 - 1000 Ti cket s shoul d show amount s t hat can be won/ l ost i n a si ngl e pl ay.

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6 • A random process is running. • It delivers many numbers. • You become confused ?!?! • No. You find some order saying that the numbers  delivered by the process vary around the  expected  value . • And the amounts are off by the size of the  standard  error.
7 • Assume a box with the tickets: 1 1 1 5 • What is the sum of 100 draws made randomly with  replacement from the box? should come up 1/4 times of total draws

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ch10 - Ch 10 TheExpectedValueand StandardError Weneed...

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