Question:
Let π1, π2, π3, π4 be a random sample of size 4 from an π(π, 1) distribution, where π β β is an unknown parameter. Let πΜ
= \(\frac{1 }{4 }β^4_{i=1} X_i\) , π(π) = π 2 + 2π and πΏ(π) be the Cramer-Rao lower bound on variance of unbiased estimators of π(π). Then, which one of the following statements is FALSE?
Let π1, π2, π3, π4 be a random sample of size 4 from an π(π, 1) distribution, where π β β is an unknown parameter. Let πΜ
= \(\frac{1 }{4 }β^4_{i=1} X_i\) , π(π) = π 2 + 2π and πΏ(π) be the Cramer-Rao lower bound on variance of unbiased estimators of π(π). Then, which one of the following statements is FALSE?
Updated On: Oct 1, 2024
- πΏ(π) = (1 + π) 2
- πΜ + π πΜ is a sufficient statistic for π
- (1 + πΜ ) 2 is the uniformly minimum variance unbiased estimator of π(π)
- πππ((1 + πΜ ) 2 ) β₯ \(\frac{(1+ΞΈ) ^2}{ 2}\)
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The Correct Option is C
Solution and Explanation
The correct option is (C): (1 + πΜ
) 2 is the uniformly minimum variance unbiased estimator of π(π)
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