Let X 1 , . . . , X n be a simple random sample from a
Question:
Consider ÏÌ2k as an estimator of Ï2.
a. Compute the bias of ÏÌ2k in terms of k. The sample variance s2 is unbiased, and ÏÌ2k = (n 1)s2/k.]
b. Compute the variance of ÏÌ2k in terms of k. Ï2 s2 = 2Ï4/(n 1), and ÏÌ2k= (n 1)s2/k.]
c. Compute the mean squared error of ÏÌ2k in terms of k.
d. For what value of k is the mean squared error of Ï2k minimized?
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(X; Σ- (-Χ. o = k
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a We denote the mean of 2 k by E 2 k The bias of 2 k is b We denote the ...View the full answer
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