Consider fitting a continuous distribution with the density f (x) = 2 exp (-0|x|) for – ∞

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Consider fitting a continuous distribution with the density
f (x)
exp (-0|x|)
2
for - 0 < x < ∞
The mean of this distribution is 0 and the variance is 20-2. 0 is the unknown parameter.
Say you observe data -1.7,1.2,-0.3,1.6,-1.3,0.1
a) Find the maximum likelihood estimate for 0.
b) Explain why you cannot use the method of moments to find an estimate by matching
the sample mean to the population mean
c) Use method of moments in some other way to estimate 0.
d) Say instead you received the data 1.7,4.5,1.2,0.3,1.6,1.3,0.1,1.6,2.5? Does this distri-
bution appear to be a good fit for the data?
Transcribed Image Text:Consider fitting a continuous distribution with the density f (x) exp (-0|x|) 2 for - 0 < x < ∞ The mean of this distribution is 0 and the variance is 20-2. 0 is the unknown parameter. Say you observe data -1.7,1.2,-0.3,1.6,-1.3,0.1 a) Find the maximum likelihood estimate for 0. b) Explain why you cannot use the method of moments to find an estimate by matching the sample mean to the population mean c) Use method of moments in some other way to estimate 0. d) Say instead you received the data 1.7,4.5,1.2,0.3,1.6,1.3,0.1,1.6,2.5? Does this distri- bution appear to be a good fit for the data?
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