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ENGRD2700_recitation6 - ENGRD2700 Basic Engineering...

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ENGRD2700 Basic Engineering Probability and Statistics Fall 2011 Recitation 6: 30 September–3 October 2011 1. We will use @RISK to examine the following common discrete distributions: Binomial, Poisson, Geo- metric, Hypergeometric. Generate the probability mass function (pmf) plot of each one in @RISK and observe what happens as you vary the parameters. Guide your investigation by thinking about the following questions. Think about what you would expect to happen given what you know about the distribution, and then see what happens on the plot. (a) How does the shape of the Binomial pmf change as n gets large? As you make p small (close to 0) or large (close to 1)? What value of p makes the distribution symmetric? (b) What happens to the Poisson pmf as λ gets very small (close to zero)? As λ gets larger and larger (starting from λ = 10, say)—in this case, what smooth curve does the plot begin to look like? Is the Poisson distribution symmetric about its mean? For example, if X Po(10), what are P ( X 14) and P ( X 6)? Recall that the variance is
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