機率論題目

f(x) = exp(-(x-θ))

Y(1) = min(X1,X2,...,Xn)

F(X) =∫(θ,X) exp(-(t-θ)) dt
　　 = 1 - exp(-(X-θ))

fY(1) (x) = n*[1-(1-exp(-(x-θ)))]^(n-1) * exp(-(x-θ))
　　　= n*exp(-n(x-θ)) , X>θ

Zn = n(Y(1) - θ)
Y(1) = Zn /n + θ
dY(1)/dZn = 1/n

f Zn(Z) = n * exp(-n(Z /n + θ - θ)) * |1/n|
　　　= exp(-Z) , Z >0

謝謝老怪物大大
也謝謝慈信大大

沒想到你們的答案一致

只是我另一位有力人士提供的答案為
Zn～Exp(λ=1)

P[Z_n > z] = P[Y_1-θ > z/n] = P[X_i > θ+z/n, i=1,2,...,n]
= { P[X_1 > θ+z/n] }^n = { exp(-z/n) }^n = exp(-z), z > 0