Thread: Expected values of ordered statistics

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!

Hey renelovexoxo.

Hint: What is the distribution of the maximum order statistic of a bunch of I.I.D uniform random variables?

In class it has always been beta from the examples, but she has never said explicitly and I'm having issues assigning parameters. I'm not sure what to do with the division by theta...