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9_19_11

9_19_11 - Mean Variance Andrew Liu Andrew Liu Mean Variance...

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Unformatted text preview: Mean, Variance Andrew Liu September 19, 2011 Andrew Liu Mean, Variance Midterm Exam 1 Review Andrew Liu Mean, Variance Midterm Exam 1 Review Quiz 2 – 9/23 (This Friday.) Covers 3-1 – 3-4. Andrew Liu Mean, Variance Review of Mean and Variance: 2-dice-throw example 0 1/36 1/18 1/12 1/9 5/36 1/6 7/36 2 3 4 5 6 7 8 9 10 11 12 Probability Range of Random Variable Probability Mass Function Andrew Liu Mean, Variance Review of Mean and Variance: 2-dice-throw example 0 1/36 1/18 1/12 1/9 5/36 1/6 7/36 2 3 4 5 6 7 8 9 10 11 12 Probability Range of Random Variable Probability Mass Function E ( X ) = 2 * 1 36 +3 * 1 18 +4 * 1 12 + ··· +12 * 1 36 = Andrew Liu Mean, Variance Review of Mean and Variance: 2-dice-throw example 0 1/36 1/18 1/12 1/9 5/36 1/6 7/36 2 3 4 5 6 7 8 9 10 11 12 Probability Range of Random Variable Probability Mass Function E ( X ) = 2 * 1 36 +3 * 1 18 +4 * 1 12 + ··· +12 * 1 36 = 7 ( make sense ?) . Andrew Liu Mean, Variance Review of Mean and Variance: 2-dice-throw example 0 1/36 1/18 1/12 1/9 5/36 1/6 7/36 2 3 4 5 6 7 8 9 10 11 12 Probability Range of Random Variable Probability Mass Function E ( X ) = 2 * 1 36 +3 * 1 18 +4 * 1 12 + ··· +12 * 1 36 = 7 ( make sense ?) . V ( X ) = E ( X 2 )- [ E ( X )] 2 = 2 2 * 1 36 + 3 2 * 1 18 + ··· + 12 2 * 1 36- 7 2 ≈ 5 . 83 . Andrew Liu Mean, Variance Review of Mean and Variance: 2-dice-throw example 0 1/36 1/18 1/12 1/9 5/36 1/6 7/36 2 3 4 5 6 7 8 9 10 11 12 Probability Range of Random Variable Probability Mass Function E ( X ) = 2 * 1 36 +3 * 1 18 +4 * 1 12 + ··· +12 * 1 36 = 7 ( make sense ?) . V ( X ) = E ( X 2 )- [ E ( X )] 2 = 2 2 * 1 36 + 3 2 * 1 18 + ··· + 12 2 * 1 36- 7 2 ≈ 5 . 83 . σ ( X ) ≈ 2 . 42 . Andrew Liu Mean, Variance Examples (cont.) Given a random variable X . Suppose its probability mass function is given as follows. f ( x ) = ( 8 7 )( 1 2 ) x , x = 1 , 2 , 3 . Calculate E ( X ) . Andrew Liu Mean, Variance Examples (cont.) Given a random variable X . Suppose its probability mass function is given as follows....
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9_19_11 - Mean Variance Andrew Liu Andrew Liu Mean Variance...

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