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1. (Simple Application of Ewens' Formula). In a population with n D 10 animals, compute the probability that there are two species, each with five animals, and the probability that there are five species, each with two animals.
2. * (Ewens' Formula). In a population with n animals, derive an expression for the probability that there are no species with strictly larger than two animals.
3. (Use Your Computer). Plot the Po´lya-Eggenberger distribution for each of the following cases and then superimpose the Beta density function f .p/ as defined in the text for each corresponding case. Comment on the accuracy.
(a) a D b D 5; c D 1; n D 10I
(b) a D b D 5; c D 1; n D 25I
(c) a D 5; b D 20; c D 5; n D 100:
Currently, quarters have weights that are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g. A vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g.
1.as part of a promotion for a new type of cracker free samples are offered to shoppers in a local supermarket. the
However, the mean ounces of ?ll μ may change from day to day, because of change of operator or adjustments in the machine. If n = 55 observations on ounces of ?ll are taken on a given day, ?nd the probability that the sample mean will be within 0...
drcatscan is an ophthalmologist who in addition to prescribing glasses and contact lenses performs laser surgery to
For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that his wife will vote in the referendum is 0.28, and the probability that both the husband and wife will vot..
What is the variance and standard deviation (of profit, NOT of tire life) for producing an all weather tire? Of producing a high performance tire?
(a) Give a 95% confidence interval for the mean ARSMA score of Mexicans. (b) What assumptions does your condence interval require?
consider a regression situation in which y hardness of molded plastic and x amount of time elapsed since termination
A researcher tested the reading ability of two groups of primary care patients. The scores on the test range from 1 to 9 with 9 indicating a high degree of reading ability and 1 very limited reading ability.
Which of the following is not a characteristic of successful Six Sigma programs? Which of the following is the most important factor associated with Design of Experiments (DOE)?
What is the probability that the auto dealer will need to order more transmissions? You should take your calculations to 4 decimal places.
Use exponential smoothing to develop simple, trend (Holt's), and seasonal models (both simple and trend) for forecasting the quarterly revenue from 1-year batteries.
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