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Question: Show that the binomial (n, p) distribution approaches the Poisson (µ) distribution as n → ∞, and p → 0 with np = µ held fixed. Consider the negative binomial distribution with parameters r and p = 1 - q. Let r → ∞, and let p → 1 so that rq = µ is held fixed.
a) What does the mean become in the l limit?
b) What does the variance become in the limit?
c) Show the distribution approaches the Poisson (µ) distribution in the limit.
Let ./{x) = !, x = 1, 2, 3, 4, 5, 6, zero elsewhere, be the p.d.f. of a distribution of the discrete type. Show that the p.d.f. of the smallest observation of a random sample of size 5 from this distribution is gl(yl) = (7 -6 Y•)s -(6 -6 Y•)s, ..
a. Calculate AOQ for p = .01, .02,..., .10. What does this suggest about the value of p for which AOQ is a maximum and the corresponding AOQL?
a field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. the
Let X be the number of cucumbers that Mimi harvests (that is, the number of cucumbers not eaten by rabbits). As we know, the distribution of X is a binomial.
Do you think an F-ratio of 1 would lead you to conclude that there is no treatment effect? Why? Justify your answers with examples.
your organization has a goal of 14 days for the average processing of a purchase request pr from notification to final
assume 85 of passengers show up 15 will not. airline booked 11 people for 10 seats.1 find probability there are enough
Focusing on Data Analysis: Using the data from Chapter 1: UWEC Undergraduates (pp. 30-31), and answer questions a,b,c,d,e,f,g (UWEC Undergraduates.
Welcome a woman taking the initiative in asking for a date. What is the probability that seven (7) of the men say NO.
With 90% confidence, compute the maximum error between the sample average of the 49 radii measurements of the previous problem and the true average radius.
What's the probability that the attorney will be selected for the next case, assuming all registered attorneys are eligible? What is the probability that her partner will be selected in this scenario? What is the probability that the attorney OR her ..
Many college students are familiar with meditation exercises. One question about meditation that has been answered is: Are there physiological effects?
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