Binomial_R_f10 - no chocolate donuts left over? By hand:...

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Statistics 3011, Course Notes Supplement 4 October 11, 2010 The Binomial Distribution in R The dbinom function Let X be a binomial random variable with number of trials n and probability of success p . That is, X Bin ( n,p ). Then dbinom(x=k, size=n, prob=p) (substitute numbers in for k, n and p) gives P ( X = k ). Example XYZ corporation has an executive board meeting tomorrow morning, and Steve is assigned the all-important task of providing the donuts. There will be 25 executives attending the board meeting. Based on past experience, Steve knows that there is a 40% chance that each executive will want a chocolate donut, and that the executives’ desires for chocolate donuts are independent of each other. Let X be the number of chocolate donuts the executives at this board meeting will want. a) What is the probability distribution of X ? b) Suppose Steve brings a dozen chocolate donuts to the meeting. What is the proba- bility that X = 12; that is, everybody who wants a chocolate donut gets one, and there are
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Unformatted text preview: no chocolate donuts left over? By hand: ConFrm your answer with R: dbinom(x=12,size=25,prob=.4) 1 Statistics 3011, Course Notes Supplement 4 October 11, 2010 The pbinom function The pbinom function computes the lower tail probability of the binomial distribution. In other words, if X Bin ( n,p ), then pbinom(q=k, size=n, prob=p) (substitute numbers in for k, n and p) gives P ( X k ). Note that P ( X k ) n = P ( X < k ), because X is discrete. Example (continued) c) If Steve brings a dozen chocolate donuts to the meeting, what is the probability that at least one executive who wants a chocolate donut does not get one? By hand: Solve the problem with R: 1 - pbinom(q=12,size=25,prob=.4) d) If Steve brings a dozen chocolate donuts to the meeting, what is the probability that there will be at least 3 chocolate donuts left over? By hand: Solve the problem with R: 2...
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Binomial_R_f10 - no chocolate donuts left over? By hand:...

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