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4 Let X1​,⋯,Xn​ be an random variables from a distribution with density (θ>0) f(x)={θ1​x(1/θ)−10​0≤x≤1 Otherwise ​ Show

Posted: Thu Jul 14, 2022 4:51 pm
by answerhappygod
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4 Let X1​,⋯,Xn​ be an random variables from a distribution with density (θ>0) f(x)={θ1​x(1/θ)−10​0≤x≤1 Otherwise ​ Show that a) Xˉ→P1+θ1​. b) Find the limiting distribution for θ^=Xˉ1−Xˉ​. (Hint: use CLT and delta method) (10 pts)