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Unformatted text preview: N = 10 + 90 = 100 , D = 10 , n = 10 (a) Let the number of defective items in the sample be X and X ∼ Hyper (10 , 10 , 100) It is a hypergeometric random variable with n = 10 , S = 10 , N = 100 i. 2 possible outcomes: defective items or nondefective items ii. f nite population without replacement, i.e. dependent trials, p is not a constant (b) The expected number of defective items in the sample is E ( X ) = n S N = 10 ∗ 100 1000 = 1 Its standard deviation is σ : r n S ( N − S ) N 2 N − n N − 1 = r 10 ∗ 10(100 − 10) 100 2 ∗ 100 − 10 100 − 1 = √ . 818182 = 0 . 904534 (c) The sample is considered to be unacceptable if it contains more than two defective items P ( x > 2) = 1 − P ( x 6 2) P ( x 6 2) = P ( x = 0) + P ( x = 1) + P ( x = 2) = 2 X x =0 C 10 x C 90 10 − x C 100 10 = 0 . 93998 P ( x > 2) = 1 − . 93998 = 0 . 06002 2...
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This note was uploaded on 01/06/2011 for the course ISOM 111 taught by Professor Hu,inchi during the Fall '10 term at HKUST.
 Fall '10
 Hu,Inchi

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