Chapter9-class

# Chapter9-class - Module 9 Topics Binomial Distribution...

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1 Module 9 Modeling Uncertainty: THEORETICAL PROBABILITY MODELS Topics Binomial Distribution Poisson Distribution Exponential Distribution Normal Distribution Beta Distribution

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2 Introduction Module 7: basic probability use in decision problems Module 8: subjective probability modeling for decision analysis Module 9: theoretical distributions application to decision analysis Module 9 software tutorial
3 Theoretical Probability Models Learning Objectives Refresh knowledge: Binomial distribution Poisson distribution Exponential distribution Normal distribution Gain knowledge: Beta distribution

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4 Binomial Distribution (a discrete distribution) Model characteristics: Dichotomous outcomes Two possible outcomes One outcome can occur Constant probability of “success” Independence
5 Binomial Distribution Mathematical model: • P B (R= r | n, p) = [ n! / r! (n - r)! ] p r (1-p) n-r B subscript = binomial probability R = binomial random variable r = number of successful outcomes n = number of events or trials p = probability of successful outcome E (R) = = np Var (R) = = np(1- p) μ σ 2

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6 Binomial Distribution Probability mass function notation: f (x) = ( ) p x q n-x X = binomial random variable x = number of successful outcomes n = number of events or trials p = probability of a successful outcome q = 1 – p = probability of an unsuccessful outcome E (X) = µ = np V (X) = σ 2 = µq n x
7 Binomial Distribution Cumulative distribution function: Probability of k or fewer “successful” outcomes F (x k) = ∑ ( ) p x q n-x k X = 0 n x

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8 Binomial Distribution Frequent application situations: Quality control Reliability Survey sampling Approximation by other models: Poisson: p → 0 and n → ∞ Normal: p 0.5 and np > 5, OR p > 0.5 and nq > 5
9 Binomial Distribution Example application: Items are manufactured in large lots, from each of which twenty units are selected at random. The lot is accepted if the sample contains three or fewer defectives. If the production process yields, on the average, ten percent defectives, what is the probability of lot acceptance?

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Binomial Distribution Formulation: Determine the probability of three or fewer “successes” in 20 independent trials, each having 0.1 probability of success. F (x
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## This note was uploaded on 12/04/2011 for the course BUSINESS 500 taught by Professor John during the Spring '11 term at Kansas.

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Chapter9-class - Module 9 Topics Binomial Distribution...

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