I'm having trouble calculating the expected value for this problem:

Let Y1; Y2; : : : ; Yn be independent and identically distributed random variables from a Uniform distribution with minimum value 1 = 0 and maximum value 2 = theta.

(b) Find the expected value of max Yi.

I found the probability density function to be^{n}/_{theta}*(^{y}/_{theta})^{n-1 }In class, everything fell into an easy distribution, and typically this became a beta distribution to find the expected values. I'm having trouble identifying the parameters. I simplified this to f(y)=^{n}/_{theta^n}* y^{n-1}but I can't seem to name the parameters. When I tried the integral, it seemed far beyond this course, especially since we didn't do any examples. Is there something I'm not seeing? Thanks!