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Statistics unbiased estimator #3 
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#1
Mar110, 06:37 PM

P: 201

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*(1F_{Y}(y))^{n1}f_{Y}(y) Y_{max}=n*(F_{Y}(y))^{n1}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 


#2
Mar110, 08:38 PM

P: 201

anybody ?
can't figure it out :\ 


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