1. Uniform distribution.

The following question has got me puzzled so if anyone could give me a start, I would be very grateful:

Suppose you choose 3 numbers at random that are uniformly distributed on the interval [0,1]. What is the expected value of the maximum of the three numbers?

2. Originally Posted by buckaroobill
The following question has got me puzzled so if anyone could give me a start, I would be very grateful:

Suppose you choose 3 numbers at random that are uniformly distributed on the interval [0,1]. What is the expected value of the maximum of the three numbers?
$\displaystyle prb(max(x_1,x_2,x_3)<a)=prb(x_1<a)prb(x_2<a)prb(x_ 3<a)=a^3$

so the pdf of $\displaystyle y=max(x_1,x_2,x_3)$ is:

$\displaystyle p(y)=\left. \frac{d}{da}a^3 \right|_{a=y},\ y \in [0,1],\ \mbox{ and }0 \mbox{ otherwise }$

RonL