6.6-4. Find the Rao-Cramér lower bound, and thus the asymptotic variance of the maximum likelihood estimator 0, if the random sample X₁, X2, ..., X is taken from each of the distributions having the following pdfs: (a) f(x;0)=(1/02)xe−x/@ (b) f(x; 0) = (1/20³) x² e-x/0, (c) f(x; 0) = (1/0)x(1-0)/8 0 < x <∞0, 0 <0 <∞0. 0

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6.6-4. Find the Rao-Cramér lower bound, and thus the
asymptotic variance of the maximum likelihood estimator
0, if the random sample X₁, X2,..., X is taken from each
of the distributions having the following pdfs:
(a) f(x;
Đ)=(1/02)xex/
0<x<∞0, 0 <0 <∞0.
(b) f(x; 0) = (1/20²³) x² e¯x/8₂ 0<x<∞0, 0 <0 <∞0.
(c) f(x; 0) = (1/0) x(1-0)/8
0 <0 <∞.
0 < x < 1,
TUS
Transcribed Image Text:6.6-4. Find the Rao-Cramér lower bound, and thus the asymptotic variance of the maximum likelihood estimator 0, if the random sample X₁, X2,..., X is taken from each of the distributions having the following pdfs: (a) f(x; Đ)=(1/02)xex/ 0<x<∞0, 0 <0 <∞0. (b) f(x; 0) = (1/20²³) x² e¯x/8₂ 0<x<∞0, 0 <0 <∞0. (c) f(x; 0) = (1/0) x(1-0)/8 0 <0 <∞. 0 < x < 1, TUS
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