Suppose we wish to study the mean u of a population r1,..., IN through simple random sampling (with replacement), but that we can only obtain a sample with some measurement error. Specifically, suppose that the true value of the simple random sample is X1,..., Xn, but that we only get to sample Y1,...,Yn, where
Suppose we wish to study the mean u of a population r1,..., IN through simple random sampling (with replacement), but that we can only obtain a sample with some measurement error. Specifically, suppose that the true value of the simple random sample is X1,..., Xn, but that we only get to sample Y1,...,Yn, where
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Transcribed Image Text:Suppose we wish to study the mean µ of a population x1,..., IN through simple random sampling
(with replacement), but that we can only obtain a sample with some measurement error. Specifically,
suppose that the true value of the simple random sample is X1,..., Xn, but that we only get to
sample Y1,..., Yn, where
Y; = X; + ei,
where e; is a measurement error with mean E(e;) = He and variance Var(e;) = o2.
а)
What is the formula for the sample mean of the simple random sample we obtain,
(1/n) Y;?
What is the expected value of the sample mean of the simple random sample we
obtain, E{(1/n) E,Yi}?
b)
c)
Under what conditions will (1/n) E-1 Yi be an unbiased estimator of µ?
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Step 1
Given information:
The investigator is specially interested to study the mean µ of the population x1, x2, … , xN.
Given that the simple random sampling with replacement gives the sample with some measurement error.
The true values of the simple random sample are X1, X2, … , Xn but the obtained sample is Y1, Y2, … , Yn, where Yi = Xi + ei.
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