Lecture29

# Lecture29 - Lecture 29 Confidence Intervals Section 8.1...

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Confidence Intervals Section 8.1 Lecture 29

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Confidence Intervals The Central Limit Theorem tells us that the average of a large number of independent, identically distributed random variables is approximately normally distributed: 2 1 1 ~, n i i X X N nn   
Example Let X be the outcome of the roll of a fair six- sided die. Then E ( X ) = 3.5 and Var ( X ) = 2.917. If we roll the die many times, then we would expect the average outcome to be close to μ = 3.5. But how close? And how certain can we be?

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Definition The number μ is an attribute of the dice. It may be unknown in practice. A fair die has μ = 3.5 but you may not be sure that the die is fair. μ is called a parameter of the distribution of X . The value depends on the experiment. If another person rolls the die many times, he may obtain a slightly different . This number is called a statistic . What allows us to do computations is that we know the distribution of the statistic.
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Lecture29 - Lecture 29 Confidence Intervals Section 8.1...

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