#### changfa

##### Advanced Member level 4

let M_K denote max(x1,x2,...,xK) and it is straight forward to show that the CDF of M_K is (F(x))^K where F(x) is the CDF of N(mu, sigma^2). Then the pdf of M_K is given by K*(F(x))^(K-1)*f(x).

The final step is to calculate the mean value of M_K as

E{M_K} = \int_{0}^{+oo} x * K*(F(x))^(K-1)*f(x) dx.

Does anyone know if there is close-form expression for this? or how to numerically calculate this integral in Matlab? (I tried but failed)

Thanks a lot!\]