ENGRD2700Basic Engineering Probability and StatisticsFall 2011Recitation 6: 30 September–3 October 20111. 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 andobserve what happens as you vary the parameters.Guide your investigation by thinking about the following questions.Think about what you wouldexpect 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 asngets large? As you makepsmall (close to0) or large (close to 1)? What value ofpmakes the distribution symmetric?(b) What happens to the Poisson pmf asλgets very small (close to zero)? Asλgets larger and larger(starting fromλ= 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, ifX∼Po(10), what areP(X≥14) andP(X≤6)? Recall that the variance is
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Probability theory, Binomial distribution, Discrete probability distribution, Binomial pmf change