a question in uniform distribution

#1
suppose X1,…,Xn be random sample of U(0,θ) distribution. if X(n) be largest order statistics of sample, and V=nX¯/X(n), how can I calculate Var(3V−X(n))
X¯ is mean of sample.
 

staassis

Active Member
#2
Use the fact that

1) conditional on X(n), the remaining (n-1) variables are distributed as U([0, X(n)]);

2) Prob(X(n) <= c) = (c/θ)^n.