9.3 Fitting a Poisson Distribution: You count the number of times that the annoying "MacSweeper" popup window appears per hour when you surf the web. You wish to model these counts with a Poisson distribution. On day 1, you surf for 4 h, and see counts of 3, 1, 4, 2 (in hours 1 through 4 respectively). On day 2, you surf for 3 h, and observe counts of 2, 1,2. On day 3, you surf for 5 h, and observe counts of 3, 2, 2, 1, 4. On day 4, you surf for 6 h, but keep only the count for all 6 h, which is 13. You wish to model the intensity in counts per hour. (a) What is the maximum likelihood estimate of the intensity for each of days 1, 2, and 3 separately? (b) What is the maximum likelihood estimate of the intensity for day 4? (c) What is the maximum likelihood estimate of the intensity for all days taken together?
9.3 Fitting a Poisson Distribution: You count the number of times that the annoying "MacSweeper" popup window appears per hour when you surf the web. You wish to model these counts with a Poisson distribution. On day 1, you surf for 4 h, and see counts of 3, 1, 4, 2 (in hours 1 through 4 respectively). On day 2, you surf for 3 h, and observe counts of 2, 1,2. On day 3, you surf for 5 h, and observe counts of 3, 2, 2, 1, 4. On day 4, you surf for 6 h, but keep only the count for all 6 h, which is 13. You wish to model the intensity in counts per hour. (a) What is the maximum likelihood estimate of the intensity for each of days 1, 2, and 3 separately? (b) What is the maximum likelihood estimate of the intensity for day 4? (c) What is the maximum likelihood estimate of the intensity for all days taken together?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:**9.3 Fitting a Poisson Distribution:** You count the number of times that the annoying “MacSweeper” popup window appears per hour when you surf the web. You wish to model these counts with a Poisson distribution. On day 1, you surf for 4 hours, and see counts of 3, 1, 4, 2 (in hours 1 through 4 respectively). On day 2, you surf for 3 hours, and observe counts of 2, 1, 2. On day 3, you surf for 5 hours, and observe counts of 3, 2, 2, 1, 4. On day 4, you surf for 6 hours, but keep only the count for all 6 hours, which is 13. You wish to model the intensity in counts per hour.
(a) What is the maximum likelihood estimate of the intensity for each of days 1, 2, and 3 *separately*?
(b) What is the maximum likelihood estimate of the intensity for day 4?
(c) What is the maximum likelihood estimate of the intensity for all days taken together?
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