a Which of the above estimators are unbiased for 0? e80.0 b Among the unbiased estimators of 0, which has the smallest variance? nseM

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 44CR
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9.1)  Suppose X1, X2, and X3, denotes a random sample from the exponential distribution with density function shown in the image.

a) Which of the above estimators are unbiased for θ?

b) Among the unbiased estimators of  θ, which has the smallest variance?

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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