1) Let X1, X2, X3 be a random sample of 3 units with a Normal distribution (N(H, o2 )) with expected value p and variance o2. The parameters u and o2 are unknown. Given the following estimators to estimate the parameter µ. Az = X, +X2 +X3 a) Show that the estimators are unbiased. b) Which of the unbiased estimators is more efficient? Show.

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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Please help me for Question 1

1) Let X1, X2, X3 be a random sample of 3 units with a
Normal distribution (N(H, o2 )) with expected value
p and variance o2. The parameters u and o2 are
unknown. Given the following estimators to
estimate the parameter µ.
Ex + ?x?+ 'x = 'v
Az =X, +X, +X3
a) Show that the estimators are unbiased.
b) Which of the unbiased estimators is more efficient?
Show.
Transcribed Image Text:1) Let X1, X2, X3 be a random sample of 3 units with a Normal distribution (N(H, o2 )) with expected value p and variance o2. The parameters u and o2 are unknown. Given the following estimators to estimate the parameter µ. Ex + ?x?+ 'x = 'v Az =X, +X, +X3 a) Show that the estimators are unbiased. b) Which of the unbiased estimators is more efficient? Show.
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,