Show that YN = Nỹn is unbiased for Yy. That is, show that E[ YN]= YN -

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.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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Suppose that the finite population being studied has N elements from which a sample of size n is drawn using SRSWOR to estimate the population total

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N
YN =
Yi
To estimate YN, the estimator YN = Ny, will be used.
Given that yn is an unbiased estimator of the population mean YN where
п
1
YN
N
Yn
= -
n
i=1
E[y] = YN, E[ In]
= YN
Show that YN
Nỹ, is unbiased for YN. That is, show that E[ YN ] = YN
Transcribed Image Text:N YN = Yi To estimate YN, the estimator YN = Ny, will be used. Given that yn is an unbiased estimator of the population mean YN where п 1 YN N Yn = - n i=1 E[y] = YN, E[ In] = YN Show that YN Nỹ, is unbiased for YN. That is, show that E[ YN ] = YN
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