Let the probability density of the population X be: F (x, θ) = e to the power of [- (x - θ)], X ≥ θ; 0, X

Let the probability density of the population X be: F (x, θ) = e to the power of [- (x - θ)], X ≥ θ; 0, X

Ex = ∫ (upper + ∞ lower θ) XF (x, θ) DX = ∫ (upper + ∞ lower θ) Xe ^ [- (x - θ)] DX
=-(Xe ^ [- (x - θ)] | (upper + ∞ lower θ) -∫ (upper + ∞ lower θ) e ^ [- (x - θ)] DX)
=-θ-1=µ
θ=-µ-1
θ ^ = -  ̄ X-1 (the left horizontal line of X is above x)
Where  ̄ x = 1 / N ∑ (from 1 to n) Xi