(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that n=5 observations are taken from the uniform pdf, f_{Y}=1/[tex]\Theta[/tex] 0<y<[tex]\Theta[/tex]

where [tex]\Theta[/tex] is unknown. Two unbiased estimators for [tex]\Theta[/tex] are

[tex]\Theta[/tex]_{1}= (6/5)*Y_{max}

[tex]\Theta[/tex]_{2}= (6)*Y_{min}

which estimator would be better to use? hint: What must be true of Var(Ymax) and Var(Ymin) given that fy is symmetric ? Does your answer as to which estimator is better make sense on intuitive grounds ? Explain.

2. Relevant equations

Var(Y)=E[Y^{2}] - E[Y]^{2}

Y_{min}=n*(1-F_{Y}(y))^{n-1}f_{Y}(y)

Y_{max}=n*(F_{Y}(y))^{n-1}f_{Y}(y)

3. The attempt at a solution

I'm trying to calculate the variances of both the estimators and see which one is smaller.

But, there is the extra information like, n=5 and that the distribution is symmetric, and I'm sure I need to use it.

Plus, I don't know how to answer it on intuitive grounds.

Would appreciate any help.

Thanks.

EDIT:

Now, I am still trying to solve it, and if I know that the distribution is symmetric, the variance of Ymin and Ymax are the same.

However, since the first estimator is divided by 5, we know that it's 1/25 of the variance of the second estimator.

Can I say this ? Is this the"on intuitive grounds" answer that they are asking ?

What about the sample size n=5 ? what do I do with it ?

Thanks

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# Statistics- unbiased estimator #3

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