Let X1, X2, . . . , Xn be a random sample from a distribution with p.d.f. f(x; θ) = θe−θx on 0 ≤ x < ∞ for θ > 0. Find the maximum likelihood estimator θb for θ.

Let X1, X2, . . . , Xn be a random sample from a distribution with p.d.f. f(x; θ) = θe−θx
on 0 ≤ x < ∞ for θ > 0. Find the maximum likelihood estimator θb for θ.