If the random variable Y denotes an individual's income, Pareto's law claims that P(Y ≥ y) = (k/y)^θ, where k is the entire population's minimum income. It follows that F_Y(y) = 1− (k/y)^θ, and, by differentiation,

f_Y(y; θ) = θk^θ(1/y)^θ+1, y ≥ k; θ ≥ 1

Assume k is known. Find the maximum likelihood estimator for θ if income information has been collected on a random sample of 25 individuals.