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IEOR 165 Lecture 3 May 28 2009

# IEOR 165 Lecture 3 May 28 2009 - Lecture Notes IEOR 165 |...

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Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry Probability Theory We collect data – define an estimator on data. But we need to figure out the statistics of the data (mean, variance, distribution) We look for the standard distributions useful for statistics. (1) Unit normal (or standard normal) distribution = - , -∞< <∞ fzz 12πexp 12z2 z If = . , . . . . = . α 0 025 then the z0 025 is where area is 0 975 So z0 025 1 96 ( ) according to table Estimator: = - z x μσn - subtract MEAN and divide by SD of x bar unit normal – to use this, we need sigma So we use s2as an estimator of σ2 - = - = - / x μsn x μσnsσ x μσns2 σ2 - = = - n 1s2σ2 k 1nxk xσ2

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Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry (2) Let z1,…,zm be m independent unit normal r.v.’s = Ezk2 1 because = - = = Varzk Ezk2 Ezk2 Ezk 1 = = - - . . xm2 k 1mzk2 chi squared r v with m degrees of freedom ( ) fxm2 x 0.01 > = PXm2 xαm α m=12 0 xαm2 . , = . x 99 122 3 571 . , = . x0 01 122 26 217 We know that = - = = k 1nxk μσ2 xn2 Exn2 n - = = - n 1s2σ2 k 1nxk xσ2 = - = - Ek 1nxk xσ2 n 1 - = - n 1s2σ2 xn 12 So: What is . . = . P3 571 x122 26 217 98 - , - - , - = - Px1 α2 n 12 xn 12 xα2 n 12 1 α - 1 α
Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry α2

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IEOR 165 Lecture 3 May 28 2009 - Lecture Notes IEOR 165 |...

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