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If X1….. Xn be iid random variables with pdf of f(x/ϒ,β)= (βϒ^β/X^ β +1) I (x>ϒ)...

If X1….. Xn be iid random variables with pdf of f(x/ϒ,β)= (βϒ^β/X^ β +1) I (x>ϒ) where ϒ>0 and β>0. Also both βand ϒ are unknown

i. Find joint sufficient statistic for (β,ϒ)

ii. Find maximum likelihood estimators of ϒ and β

iii. A given fixed e∈( 0,1), find the MLE of d where e = P (X₁<d)

iv. If β> 2, Find methods of moment estimator of β, and ϒ

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