The time X to the first click on Geiger counter has exponential distribution f(x)=e^-x , x>0. The time Y from the first click to the second has the same exponential distribution as X and is independent of X.

1. write down the joint p.d.f. of X and Y and show that, for t>0,

P(Y<tX) = t/(1+t) and

2. deduce that, for 0<u<1; P(X/(X+Y)<u)=u

3. interpret the result in 2 above...