10-49. Let {X1,X2, . . . ,Xn} represent a set of sample random variables drawn from the probability density function f (x; θ1, θ2) = - 1

θ2 e−(x−θ1)2/θ2 , −∞ < θ1 ≤ x < +∞, 0 < θ2 < +∞, 0 elsewhere.

Find maximum likelihood estimates for θ1 and θ2. Are these estimates jointly sufficient statistics?