From last event to this event = 10, from this event to next event = 10, so the time between the first and the third event is 20, where is the surprise in the Waiting Time Paradox?, sure I must be missing some key ingredient here.
The random moment we picked in time is not necessarily an event. The expected time between the event to your left and the one to your right (they're consecutive) is 20 minutes.
I think we must use conditional probability, that is the integral of p(X|A)P(A), for example probability the prior event was 5 minutes ago probabity(the next one is 10 minutes from the previous one (that is 1/2). This is like markov chain, probability of next state depends of current state.
