7) Let X₁, X2,...Xn i.i.d random sample from U(0, 0). Consider two estimators of 6₁ = 2X₂ and 6₂ = (2+¹)X(n) 62 a) Show that both the estimators are unbiased for 0. b) Show that both the estimators are consistent for 9.
7) Let X₁, X2,...Xn i.i.d random sample from U(0, 0). Consider two estimators of 6₁ = 2X₂ and 6₂ = (2+¹)X(n) 62 a) Show that both the estimators are unbiased for 0. b) Show that both the estimators are consistent for 9.
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.CR: Chapter 13 Review
Problem 42CR
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Step 1: To find the expected value of the mati mum order statistic we first find its cumulative (CDF)
VIEWStep 2: Now, since X1, X2 ... Xn are i.id random samples from V (0, θ), we have
VIEWStep 3: Final answer. Therefore,both of our estimators are unbiased as well as consistent for θ
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