In part (iii) of this question, we are asked to solve 3px(1,2) in the 2 state (1,2) model What we have found is that: mu(1,2) = 0.2 mu(2,1) = 0.8 Using this, I have calculated P(1,1) = exp(-0.2) & P(1,2) = 1 - P(1,1) = 1 - exp(-0.2) P(2,2) = exp(-0.8) & P(2,1) = 1 - P(2,2) = 1 - exp(-0.8) The probability matrix will be of the form: P = 0.8187 0.1813 0.55 0.45 therefore won't 3px(1,2) = P^3[1,2] = 0.242827 ? But it doesn't match with the answer given. Could someone please explain what I am doing wrong? Thanks
Hi George Looks like you may be mixing up Markov chains with Markov jump processes. Here we have continuous rather than discrete time. I think you may also be mixing up occupancy probabilities with more general transition probabilities. Here we have the following occupancy probabilites: \( p_{\bar{1,1}}(t) = exp(-0.2 * t) \) \( p_{\bar{2,2}}(t) = exp(-0.8 * t) \) However, we want \( p_{1,2}(3) \). To find a general formula for \( p_{1,2}(t) \), we can solve its forward differential equation. Hope this helps! Andy
