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

Let X_{1}, X_{2},....X_{n}be a random sample from pdf,

f(x|θ) = θx^{-2}where 0 < θ ≤ x < ∞

Find the MLE of θ

My attempt:

Likelihood fxn: L(θ|x) = ∏θx^{-2}= θ^{n}∏ θx^{-2}

And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get: n/θ = 0

However, I realize that θ ≤ x and θ > 0...what do I need to do to incorporate this to my likelihood function?

In class we discuss about Fisher Information and I have a guess that it has some involvement with this problem, but I'm not sure why and what we can use Fisher Information for this problem?[/SUP][/SUP][/SUP][/SUP][/SUB][/SUB][/SUB]

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# Maximum Likelihood and Fisher Information

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