9. In a batting cage, a young future slugger is swinging for the cheap seats-counting the number of pitches from one "home run" (in her mind) to the next: for instance, if she counts 4, it means it took her 4 pitches to get her first home run after she hit the last one. For 20 independent "home runs," her counts were: 3, 6, 2, 16, 12, 4, 4, 5, 15, 11, 3, 3, 2, 1, 8, 11, 5, 1, 2, 1. Assuming that these data can be looked upon as a random sample from a geometric population, a) Derive the maximum likelihood estimator for the geometric distribution's parameter 0.
9. In a batting cage, a young future slugger is swinging for the cheap seats-counting the number of pitches from one "home run" (in her mind) to the next: for instance, if she counts 4, it means it took her 4 pitches to get her first home run after she hit the last one. For 20 independent "home runs," her counts were: 3, 6, 2, 16, 12, 4, 4, 5, 15, 11, 3, 3, 2, 1, 8, 11, 5, 1, 2, 1. Assuming that these data can be looked upon as a random sample from a geometric population, a) Derive the maximum likelihood estimator for the geometric distribution's parameter 0.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:9. In a batting cage, a young future slugger is swinging for the cheap seats-counting the number of pitches
from one "home run" (in her mind) to the next: for instance, if she counts 4, it means it took her 4 pitches to
get her first home run after she hit the last one. For 20 independent "home runs," her counts were: 3, 6, 2,
16, 12, 4, 4, 5, 15, 11, 3, 3, 2, 1, 8, 11, 5, 1, 2, 1. Assuming that these data can be looked upon as a random
sample from a geometric population,
a)
Derive the maximum likelihood estimator for the geometric distribution's parameter 0.
b)
Estimate the parameter for the population the given sample was drawn from. Interpret your result
(this interpretation should include what the pertinent population is for this problem; what, then, the
parameter would represent, etc.)
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