Question

Let X1,...,Xn be a random sample from the pdf f(x;θ) = θx^(θ−1) , 0 ≤ x ≤ 1 , 0 < θ < ∞ Find the method of moments estimator of θ.

Answer #1

Given pdf:

0 x1

0 < <

between the limits 0 to 1.

Applying limts, we ge:

So, we can stimate with:

So,

The method of moments estimator of is given by:

,

where is the sample mean given by:

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Let {X1, ..., Xn} be i.i.d. from a distribution with pdf f(x; θ)
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