Hey, I need help from you on another problem.
Let X1, ... , Xn ~(iid, independent and identical distribution) Beta(Alpha, 1)
(a) Prove that X(n), the maximum of random variable Xi, also has a Beta Distribution and identify its parameter.
(b) Based on (a), What is E(X(n))?
I'm very sorry that I don't know how to write equation as others.
Anyway, let me show your work.
Let X(n)= A.
Then, FA(a), F of A of a = [FX(a)]^n , F of X of a to the n.
And fA(a)=n(FX(a))^(n-1)*fX(a)
But I can't find FX(a).
THank you.
892king