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Let X_1 and X_2 be independent random variables with

mean μ and variance σ^2.

[itex]\Theta[/itex] = ( X_1 + 3X_2 ) /4

a) is it unbiased?

b) what is the variance of the estimator?

c) what is the mean squared error of the estimator?

since there are four things, divided by 4, it is unbiased.

Then the variance is E[ (X1 + 3X2/4) - μ]^2 + [(X1+3X2/4) - μ)^2

and while expanding this, I got stuck when it was time "get the stuff out of E"

Can anyone help me with this? I have been searching (book has one paragraph long explanation) for many hours, but no avail.

Thank you

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# Mean Squared Error of an estimator.

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