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# W9-slides1 - Lecture 25 Outline and Examples Expectation...

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Lecture 25- Outline and Examples Expectation, Covariance, Variance and Correlation (Ross § 7.4)

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Expectation Example. Sample mean. Let X 1 , X 2 , ··· , X n be independent and identically distributed (i.i.d.) random variables having common distribution function F and expected mean μ . Such a sequence of random variables is said to constitute a sample from the distribution F . The quantity ¯ X = n X i =1 X i n is called the sample mean . Compute E [ ¯ X ]. Solution.
Example. Sample mean. Let X 1 , X 2 , ··· , X n be independent and identically distributed (i.i.d.) random variables having common distribution function F and expected mean μ . Such a sequence of random variables is said to constitute a sample from the distribution F . The quantity ¯ X = n X i =1 X i n is called the sample mean . Compute E [ ¯ X ]. Solution. E [ ¯ X ] = E " n X i =1 X i n # = 1 n E " n X i =1 X i # = 1 n n X i =1 E [ X i ] = μ since E [ X i ] μ. The expected value of the sample mean is

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W9-slides1 - Lecture 25 Outline and Examples Expectation...

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