Let Y, Y2,..., Y, be a random sample from a distribution with E(Y) = and...
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Let Y₁, Y2,..., Y, be a random sample from a distribution with E(Y) = μ and Var(Y₂) = n o² > 0 for i=1,2,..., n. Consider the following estimators of μ: Ĥ₂ Ĥ₁ = Yn n+ 1. n i=1 Y₁ a. Show that ₁ is unbiased estimator for μ but ₂ is biased. b. Find the efficiency of ₁ relative to 1₂. c. Are ₁ and ₂ consistent for µ? d. What can you conclude from the above results? Let Y₁, Y2,..., Y, be a random sample from a distribution with E(Y) = μ and Var(Y₂) = n o² > 0 for i=1,2,..., n. Consider the following estimators of μ: Ĥ₂ Ĥ₁ = Yn n+ 1. n i=1 Y₁ a. Show that ₁ is unbiased estimator for μ but ₂ is biased. b. Find the efficiency of ₁ relative to 1₂. c. Are ₁ and ₂ consistent for µ? d. What can you conclude from the above results?
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Mathematical Statistics With Applications In R
ISBN: 9780124171138
2nd Edition
Authors: Chris P. Tsokos, K.M. Ramachandran
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