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categoryالرياضيات
schoolبكالوريوس
event_available2026-07-14
السؤال
Transcribed Image Text:
Questions 18 and 19 are based on the following information.
A random variable X has mean μ and variance o². A random sample of 2 observations is taken from
the probability distribution of X, resulting in sample random variables X₁ and X2. A researcher
proposes the following four estimators of μ:
X = X₁+X₂
W=X₁
2
G=0.3X+0.7X2
Z=0.64X+0.35X2
18. Which of these estimators is an unbiased estimator of μ?
a. W only
b. Z only
c. X and G
d.
X, W and G
e.
None, all are biased.
19. Of the unbiased estimators, the most efficient is:
a.
X
b. W
c. Z
d. G
e. None of the above, they all have equal variance.
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