W4-slides1 - defective items in a sample of 200 items...

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Lecture 7- Outline and Examples Discrete probability distributions -Poisson -Geometric -Negative Binomial
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Poisson distribution ( Ross chapter 4) Example. Defective in a sample. Problem. Suppose that over the long run a manufacturing process produces 1% defective items. What is the chance of getting two or more defective items in a sample of 200 items produced by the process?
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Poisson distribution ( Ross chapter 4) Example. Defective in a sample. Problem. Suppose that over the long run a manufacturing process produces 1% defective items. What is the chance of getting two or more
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Unformatted text preview: defective items in a sample of 200 items produced by the process? Solution. We assume that each item is defective with probability p = 1 / 100, independently of other items. Let X be the number of defectives in a sample of 200. Then X ∼ Bin ( n = 200 , p = 1 / 100) with np = 200 × 1 / 100 = 2. Using Poisson approximation, P ( X ≥ 2) = 1-P ( X = 0)-P ( X = 1) ≈ 1-e-2 2 0!-e-2 2 1 1! = 1-3 e-2 = 0 . 594 ....
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This note was uploaded on 06/05/2010 for the course STAT PStat 120a taught by Professor Rohinikumar during the Spring '10 term at UCSB.

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W4-slides1 - defective items in a sample of 200 items...

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