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Statistics / Probability and Statistical Inference 9 / Chapter 6.4 / Problem 6.4-3

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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A random sample X1, X2, ... , Xn of size n is taken from a Poisson distribution with a

Chapter 6, Problem 6.4-3

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QUESTION:

A random sample X1, X2, ... , Xn of size n is taken from a Poisson distribution with a mean of , 0 << . (a) Show that the maximum likelihood estimator for is 6 = X. (b) Let X equal the number of flaws per 100 feet of a used computer tape. Assume that X has a Poisson distribution with a mean of . If 40 observations of X yielded 5 zeros, 7 ones, 12 twos, 9 threes, 5 fours, 1 five, and 1 six, find the maximum likelihood estimate of .

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QUESTION:

A random sample X1, X2, ... , Xn of size n is taken from a Poisson distribution with a mean of , 0 << . (a) Show that the maximum likelihood estimator for is 6 = X. (b) Let X equal the number of flaws per 100 feet of a used computer tape. Assume that X has a Poisson distribution with a mean of . If 40 observations of X yielded 5 zeros, 7 ones, 12 twos, 9 threes, 5 fours, 1 five, and 1 six, find the maximum likelihood estimate of .

ANSWER:

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The poisson distribution is,

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