I dont know how to compute or prove the following
Let X_1,...X_n be IID pos. valued RV and P(X_i > x) = 1\(1+x^a) for all i=1,....n, and let Y_n = max{X1,....,X_n}
First, for any natural number m, whats the condition of "a" so that E[Y_2^m] < inf, so basically when are the moments of Y_2 finit.
P(Y_2<x) should be (x^(2a))/(1+x^a)^2, but I dont know how to integrate that...? (Or is there another efficent method to show it?)
Second, how to show the equality between E(Y_n^m) < inf <=> E(X_1^m) < inf.
Any help much appreciated!
Let X_1,...X_n be IID pos. valued RV and P(X_i > x) = 1\(1+x^a) for all i=1,....n, and let Y_n = max{X1,....,X_n}
First, for any natural number m, whats the condition of "a" so that E[Y_2^m] < inf, so basically when are the moments of Y_2 finit.
P(Y_2<x) should be (x^(2a))/(1+x^a)^2, but I dont know how to integrate that...? (Or is there another efficent method to show it?)
Second, how to show the equality between E(Y_n^m) < inf <=> E(X_1^m) < inf.
Any help much appreciated!