Let X1, X2, ... Xn be independent, uniformly distributed random variables on the interval [0, theta].

a.) Find the c.d.f. of Yn = max(X1, X2, ..., Xn).

b.) Find the p.d.f. of Yn = max(X1, X2, ..., Xn).

c.) Find the mean and variance of Yn = max(X1, X2, ..., Xn).

d.) Suppose that the number of minutes that you need to wait for a bus is uniformly distributed on the interval [0, 15]. If you take the bus five times, what is the probability that your longest wait is less than 10 minutes?

e.) Find the p.d.f. of Yr, the rth-order statistic, where r is an integer between 1 and n.

f.) Find the mean of Yr.

For part a, I got the c.d.f of Yn = [F(y)]^n

For part b, I got the p.d.f pf Yn = g(y) = n*[F(y)]^(n-1) * f(y)

I'm not sure if I am doing this right. And I'm lost for the rest of the problem with what to do.