Originally Posted by

**lllll** You and N of your friends are meeting for dinner, where N is a Poisson random variable with $\displaystyle \lambda=10$. All of you arrive independently and according to a uniform distribution over (0,1). Find the expected number of friends that arrive before you.

my book has an example, but they skip a lot of steps, so all I have is:

$\displaystyle \int_0^1 E[N](t) \cdot 1 dt$ and they conclude that it's $\displaystyle \frac{\lambda}{2}$ but I'm a little lost at picking my E[N](t)