问个概率问题

Y=max(X1,X2,,,Xn)
F_Y(y)=n*F_X(y)^(n-1)*f_X(y)

This a classical theory, the order statistics of i.i.d.
exponential distribtuion is Beta distribution

oh, where can I find this classical theory?

Extreme Value Theory

Beta Distribution?
when K is relatively large, max(exp) can be approximated by Gumbel type
extreme distribution whose CDF is like exp(-exp(x))

接着上面的问题再向大家请教下
A={a1,a2,...an},其中每个元素都服从指数分布；B={b1,b2,...bn}中每个元素也服从莫
指数分布，那么maxmin{ak,bk}, k=1,2,..n服从的分布据我知道是可以求出来的。但这
是反过来求ak或bk的分布可以吗？