I am not getting the work done in RHS in the attached file's proof. I didn't get any of the equalities.
this is showing that when we jump, the state we go has nothing to do with how long we've spent where we are. eg stay healthy for 10 years, leave H state, do we die? do we get sick? Who knows? Well, whatever the chances of each, it is irrelevant that we were healthy for 10 years. The equalities rely on Bayes' theorem, that P[A and B] = P[A] * P[B|A] Good luck! John