probability question

[Guest roger]

i cant figure out this question. N people playing a game, and X_i is the score of the ith person. assume X_i are independent with density f(x)=2x for 0<x<1; and f(x)=0 otherwise. High score wins. What is the expected value of the winner's score?

 

thanks in advance

[Tartaglia]

P (winner < x) = x^2n

therefore F(x) = X^2n

therefore f(x) = 2n*x^(2n-1)

E(X) = integrate between 1 and 0 f(x) * x dx

E(X) = 2n/2n+1