10-48. Suppose {X1,X2, . . . ,Xn} represents a set of sample random variables drawn from each of the following probability density functions. Find a maximum likelihood estimator of θ:

(a) f (x; θ) = 1

θ x 1

θ

−1, 0 < x < 1,θ > 0

(b) f (x; θ) = θxθ−1, 0 ≤ x ≤ 1,θ > 0

(c) f (x; θ) = 1

θ2 xe−x/θ , x > 0,θ > 0