(Answered) Find the Method of Moments estimator

Statistics

The Pareto distribution has a probability density function:

f(x) = θα^θx^-θ-1 , x >= α, θ > 1

where α and θ are positive parameters of the distribution. Assume that α is known and that X₁, ..., X_n is a random sample of size n.

a) Find the Method of Moments estimator for θ.

b) Find the maximum likelihood estimator for θ. Does this estimator differ from that found in part (a)?

c) Estimate θ based on these data (using both methods):

3, 5, 2, 3, 4, 1, 4, 3, 3, 3

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