ioe265f11-Lec07 - Lec 07 - Binomial Distribution Topics...

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Lec 07 - Binomial Distribution IOE 265 F11 1 1 Binomial Distribution 2 Topics I. Binomial experiments II. Binomial random variables III. Hypergeometric, geometric, and negative binomial distributions
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Lec 07 - Binomial Distribution IOE 265 F11 2 3 I. Binomial experiments A binomial experiment meets the following characteristics: n trials, fixed in advance Identical trials, with only 2 possible outcomes (Bernoulli trial) Independent trials Probability of success ( p ) is constant 4 Examples Flipping a coin 10 times Testing a cell phone network for transmission or connection errors Testing a sample of air for a particular pollutant Number of female births at a hospital
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Lec 07 - Binomial Distribution IOE 265 F11 3 5 II. Binomial random variables A binomial random variable is associated with a binomial experiment with n trials and is defined as trials the among successes of number the n X 6 Probability mass function The pmf of a binomial random variable is denoted in terms of parameters: n (number of trials) and p (probability of success)   otherwise 0 , , 2 , 1 , 0 1 , ; n x p p x n p n x b x n x EXCEL: =binomdist(x,n,p,false) for pmf for cdf use “true”
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Lec 07 - Binomial Distribution IOE 265 F11 4 7 Example Air pollution monitoring in a big city is underway. Suppose there is a 10% chance of finding a high concentration of ozone. You take 18 samples. What is: Pr(exactly 2 samples will have it)=? Pr(at least 4)=? Pr(at least 3 but at most 6)=? 8 Binomial tables Table A.1 in textbook tabulates the binomial cdf F(X) for n =5, 10, 15, 20, 25 with selected values of p      n x p n y b p n x B x X P p n Bin X x y , , 1 , 0 , ; , ; , ~ 0
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This note was uploaded on 01/05/2012 for the course IOE 265 taught by Professor Jin during the Fall '07 term at University of Michigan.

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ioe265f11-Lec07 - Lec 07 - Binomial Distribution Topics...

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