Question

P2.10 Interview question Two people, trying to meet, arrive at times independently and uniformly distributed between noon and 1pm. Find the expected length of time that the first waits for the second.

Answer 1

let

X = time of arrival of people 1

Y = time of arrival of people 2

X,Y = Unif(0,1)

we need to find

E(max(x,y) - min (x,y))

f(x,y) = 1

$\int _0^1\:\int _0^1\:max\left(x,\:y\right)-\:min\:\left(x,\:y\right)\:dx\:dy = 1/3$

= 20 min