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1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μ and V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean: ˆμ1 = (n −3/n) ̄X ˆμ2 = 0.95 ̄X (a) Which of the estimators is an unbiased estimator for μ? (b) Which is the variance of the two estimators? (c) Given the properties above, which one would you prefer? Is there another property that would influence your decision? Explain.

1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μ and V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean: ˆμ1 = (n −3/n) ̄X ˆμ2 = 0.95 ̄X (a) Which of the estimators is an unbiased estimator for μ? (b) Which is the variance of the two estimators? (c) Given the properties above, which one would you prefer? Is there another property that would influence your decision? Explain.

Calculus For The Life Sciences
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.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μ
and V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean:
ˆμ1 = (n −3/n) ̄X
ˆμ2 = 0.95 ̄X
(a) Which of the estimators is an unbiased estimator for μ?
(b) Which is the variance of the two estimators?
(c) Given the properties above, which one would you prefer? Is there another property that would
influence your decision? Explain.

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