(solution) Let x1,x2,…,xn be a random sample from a unif(0,theta)

(solution) Let x1,x2,…,xn be a random sample from a unif(0,theta)

Let x1,x2,…,xn be a random sample from a unif(0,theta) distribution. Then, if Y=max(Xi) and T= Y/theta , T is distributed with fnT(t)= nt^n-1 for 0<t<1   

Consider the interval estimator theta of of the form (Y+c, Y+d) where 0<=c<d and c,d are constants.

i. Given the relationship between y and theta explain why an interval of this form is plausible.

ii. Find P(Y+c<theta<Y+d)

iii. Find lim as theta goes to infinity of P(Y+c<theta<Y+d). What does this say about this form of an interval estimator in this case?