Hello all Confused by CT4 ASET question SEP06 A2 (iii) and solution. Two-state homogeneous Markov model, with transition rate σ from state A to state B. Question (iii) reads: "If σ=3, find the value of t such that the probability that no transition to state B has occurred until time t is 0.2" The solution states the probability is found by evaluating P[Waiting time > t] = 0.2, but I thought it was P[Waiting time < t]. And now I don't know why I even though that. Can someone help me understand this. I know it has to do with the density function, but it's the direction of the sign that I can't figure out. Thanks Jon
S06 A2 Jon, When you say that you don't know why you thought that, I don't either! If no transition has occurred by time t then we are still waiting for the first transition. P[Ti>t] = P[staying in state i for time period t] In the alive-dead model, if the grim reaper is still waiting for a person to die, then that person must have stayed in the alive state! Exercise for you to practise this principle: Prove that, for a time-homogenous Poisson process rate lamda, the waiting times are exponentially distributed with parameter lambda. {Hint: start by proving the prob of staying in any state for a time period of t is e^minus lambda t} Give us a ring if you get stuck 01707 275776 Good luck! John
John Got it, we're waiting for the waiting time variable to be greater than t and looking for the value of this t that makes this probability 0.2. It's too much waiting around for me. Thanks very much. Jon
