Q.1. Let X= (Xı, ..Xn) be a random sample of random variables with probability density fe. Find an MLE (maximum likelihood estimator) of 0 in each of the following cases. (a) fax) = 0 'I1..e;(x), 0 is an integer between 1 and 60. (b) fAx) = e &-0M@(x), 0 > 0. f,(x)=: (c) 1-0 (o.) (x), 0E (d) fdx) = fx² I (a(x), 0 > 0. %3D

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Q.1. Let X= (X1, .Xx) be a random sample of random variables with probability density fo.
Find an MLE (maximum likelihood estimator) of 0 in each of the following cases.
(a) fdx) = 0'I{1..0,(x), 0 is an integer between 1 and 60.
(b) fa(x) = e (*-(a,)(x), 0 > 0.
(x-0)
f,(x) =.
(c)
20-1)(1-0) 1
1-0
(d) fdx) = ex? 1 (@(x), 0> 0.
Transcribed Image Text:Q.1. Let X= (X1, .Xx) be a random sample of random variables with probability density fo. Find an MLE (maximum likelihood estimator) of 0 in each of the following cases. (a) fdx) = 0'I{1..0,(x), 0 is an integer between 1 and 60. (b) fa(x) = e (*-(a,)(x), 0 > 0. (x-0) f,(x) =. (c) 20-1)(1-0) 1 1-0 (d) fdx) = ex? 1 (@(x), 0> 0.
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