two numbers chosen from 0 to 1, expected val of larger number If I pick two numbers in the interval (0,1), what is the expected value of the larger number?
Please help. I know that the expected value of one number is 0.5 but I'm not sure how to find the expected vlaue of the larger number here.

Assume that the value of the larger number is $x$. The probability of this is equal to the probability that the other number is less than $x$. This probability is obviously $x $. Therefore the expected value of the larger number is:
$$2\int_0^1 x\cdot x\, dx=\frac23,
$$
where the factor 2 counts the ways to choose the larger number.
