Let X₁,..., Xn be a random sample from a geometric distribution, X~ GEO(p). Here, P [X = x] = p(1 − p)*-1 for x = = 1, 2,... The method of moments estimator for is X Ο }Σ 1X i=1 1 n n i=1 Σ None of the other answers e-Xi

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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Let X₁,..., Xn be a random sample from a geometric distribution, X GEO(p). Here,
P[X = x] = p(1 − p)*−¹ for x
x-1
-
1, 2, ...
The method of moments estimator for is
O X
01/1X²
Ο Σ e-X
n
i=1
е
O None of the other answers
Transcribed Image Text:Let X₁,..., Xn be a random sample from a geometric distribution, X GEO(p). Here, P[X = x] = p(1 − p)*−¹ for x x-1 - 1, 2, ... The method of moments estimator for is O X 01/1X² Ο Σ e-X n i=1 е O None of the other answers
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Follow-up Question
Let X₁,..., Xn be a random sample from a geometric distribution, X~ GEO(p). Here,
-1
P[X = x] = p(1 − p)*−¹ for x =
The method of moments unbiased estimator for Var [X]
None of the other answers
·Σ" (X; – X)²
i=
X²
n
1 [X² -x]
= 1, 2,...
n+1
=
1-p
p²
is
Transcribed Image Text:Let X₁,..., Xn be a random sample from a geometric distribution, X~ GEO(p). Here, -1 P[X = x] = p(1 − p)*−¹ for x = The method of moments unbiased estimator for Var [X] None of the other answers ·Σ" (X; – X)² i= X² n 1 [X² -x] = 1, 2,... n+1 = 1-p p² is
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