Suppose X1,  X2, X3 denote a random sample from the exponential distribution with density function.   Please at the image for the full questions

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Suppose X1,  X2, X3 denote a random sample from the exponential distribution with density function.

 

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9.1
Suppose X1, X2, X3 denotes a random sample
from the exponential distribution with density
function
x> 0
re
ailgmea od T.E. (x) =
0
elsewhere
e-irto) be
2691 Consider the following four estimators of 0:
oldigilgarô, = X,
tib ziô,
X1 + X2
sl 101
%3D
X, + 2X2
Ôg =
3
Ôg = X
a Which of the above estimators are unbiased
for 0?
b Among the unbiased estimators of 0, which
has the smallest variance?
1seM
2.
Transcribed Image Text:9.1 Suppose X1, X2, X3 denotes a random sample from the exponential distribution with density function x> 0 re ailgmea od T.E. (x) = 0 elsewhere e-irto) be 2691 Consider the following four estimators of 0: oldigilgarô, = X, tib ziô, X1 + X2 sl 101 %3D X, + 2X2 Ôg = 3 Ôg = X a Which of the above estimators are unbiased for 0? b Among the unbiased estimators of 0, which has the smallest variance? 1seM 2.
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