Suppose that the interval between eruptions of a particular geyser can be modelled by an exponential distribution with an unknown parameter 0 > 0. The probability density function of this distribution is given by f(x: 0) = 0e-8, I > 0. The four most recent intervals between eruptions (in minutes) are ₁ = 32, 72 = 10, 23=28, 24 = 60; their values are to be treated as a random sample from the exponential distribution. (a) Show that the likelihood of based on these data is given by L(0) = 0¹-1300 (b) Show that L'(0) is of the form L'(0)=0³e-1300 (4) (4-1300). (c) Show that the maximum likelihood estimate of based on the data is 0.0308 making your argument clear.
Suppose that the interval between eruptions of a particular geyser can be modelled by an exponential distribution with an unknown parameter 0 > 0. The probability density function of this distribution is given by f(x: 0) = 0e-8, I > 0. The four most recent intervals between eruptions (in minutes) are ₁ = 32, 72 = 10, 23=28, 24 = 60; their values are to be treated as a random sample from the exponential distribution. (a) Show that the likelihood of based on these data is given by L(0) = 0¹-1300 (b) Show that L'(0) is of the form L'(0)=0³e-1300 (4) (4-1300). (c) Show that the maximum likelihood estimate of based on the data is 0.0308 making your argument clear.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:Suppose that the interval between eruptions of a particular geyser can
be modelled by an exponential distribution with an unknown parameter
0 > 0. The probability density function of this distribution is given by
f(x: 0) = 0e-8, I > 0.
The four most recent intervals between eruptions (in minutes) are
₁ = 32, 72 = 10, 23=28, 24 = 60;
their values are to be treated as a random sample from the exponential
distribution.
(a) Show that the likelihood of based on these data is given by
L(0) = 0¹-1300
(b) Show that L'(0) is of the form
L'(0)=0³e-1300 (4)
(4-1300).
(c) Show that the maximum likelihood estimate of based on the
data is 0.0308 making your argument clear.
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