The Pareto distribution has a probability density function:

f(x) = x^--1, x >=, > 1

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

a) Find the Method of Moments estimator for.

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

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

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