This problem is concerned with the properties of a random sample from a population with mean μ and variance ². Consider X; is a normally distributed random variable with mean ux and variance ox². Now, consider W as an alternative estimator of the population parameters, where W = ₁k₁ X₁. It is known that based on a mutually independent sample size of n=3, W is an unbiased esitmator of population mean μ, and that k₁ = 1/4, k₂ = 1/2, and k3 = 1/4. The variance of W is equal to [var]

MATLAB: An Introduction with Applications
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This problem is concerned with the properties of a random sample from a population with mean μ and
variance o².
Consider X; is a normally distributed random variable with mean µx and variance ox².
Now, consider W as an alternative estimator of the population parameters, where W = ₁ kį Xį .
It is known that based on a mutually independent sample size of n=3, W is an unbiased esitmator of
population mean µ, and that k₁ = 1/4, k₂ = 1/2, and k3 = 1/4.
The variance of W is equal to [var]
Transcribed Image Text:This problem is concerned with the properties of a random sample from a population with mean μ and variance o². Consider X; is a normally distributed random variable with mean µx and variance ox². Now, consider W as an alternative estimator of the population parameters, where W = ₁ kį Xį . It is known that based on a mutually independent sample size of n=3, W is an unbiased esitmator of population mean µ, and that k₁ = 1/4, k₂ = 1/2, and k3 = 1/4. The variance of W is equal to [var]
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