Let X1,...,X7 be a random sample from a population with mean µ and variance σ2. Consider the following estimators for µ: ˆ Θ1 = X1 +···+ X7 7 , ˆ Θ2 = 2X1 −X6···+ X4 2 . Compute the variance of the estimators. A. V[ˆ Θ1] = σ2/7, V[ˆ Θ2] = 3σ2/2 B. V[ˆ Θ1] = 3σ2/2, V[ˆ Θ2] = 3σ2/7 C. V[ˆ Θ1] = σ2/49, V[ˆ Θ2] = 3σ2/2 D. V[ˆ Θ1] = σ2/49, V[ˆ Θ2] = 3σ2/2 E. none of the above

Let X1,...,X7 be a random sample from a population with mean µ and variance σ2. Consider the following estimators for µ: ˆ Θ1 = X1 +···+ X7 7 , ˆ Θ2 = 2X1 −X6···+ X4 2 . Compute the variance of the estimators. A. V[ˆ Θ1] = σ2/7, V[ˆ Θ2] = 3σ2/2 B. V[ˆ Θ1] = 3σ2/2, V[ˆ Θ2] = 3σ2/7 C. V[ˆ Θ1] = σ2/49, V[ˆ Θ2] = 3σ2/2 D. V[ˆ Θ1] = σ2/49, V[ˆ Θ2] = 3σ2/2 E. none of the above

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

B. V[ˆ Θ1] = 3σ2/2, V[ˆ Θ2] = 3σ2/7

C. V[ˆ Θ1] = σ2/49, V[ˆ Θ2] = 3σ2/2

D. V[ˆ Θ1] = σ2/49, V[ˆ Θ2] = 3σ2/2

E. none of the above

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