Let X1, X2, ..., Xn be iid with pdf f(x|θ) = θ*x(θ-1). a) Find the Maximum...

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Let X₁, X₂, ..., X_n be iid with pdf f(x|θ) = θ*x^(θ-1). a) Find the Maximum Likelihood Estimator of θ, and b) show that its variance converges to 0 as n approaches infinity.

I have no problem with part a, finding the MLE of θ. However, I'm having some trouble with finding the variance.

The professor walked us through part b generally, but I need help with univariate transformation for sigma(-ln(x_i)) (see picture below - the professor used Y=sigma(-ln(x)), and w=sigma(Y_i). I need help particularly with the w=signma(Y_i) transformation.

Let Y -Inx

math Statistics-And-Probability

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Answer 1

Answer #1

Nouw, hele you anume Y n erbonen y1 艸-R29 KI us ellbSeelow exponential ( ⅛.) My.( ) tw

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Answer 2

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