Hi all, Am just doing this question, to answer i used A=p_ij*lamda_i, therefore was able to obtain the probability matrix P from A for all non diagonal elements by A_ij/lambda_i and then for the diagonals just took whatever value would satisfy the requirement for rows to add to 1. But the answer is wrong, and the notes do a much longer and different method using kolmogorovs equations - does anyone understand why my method isnt valid? Thanks,
Hi Molly I think you're mixing up jump chain probabilities and generic transition probabilities. The expression mu_ij / lambda_i gives us the probability of jumping to State j when leaving State i but this is not at a specific time. The question is asking for the distribution after one unit of time has elapsed. If we consider the Markov chain underlying the MJP, we can think of these types of probabilities (the mu_ij / lambda_i) as being the one-step transition probabilities. However, this is not the same as the one-time-unit transition probabilities in the MJP itself (as the underlying Markov chain ignores actual timings of the jumps). To calculate p_ij(1), we need to take the approach in the solutions. Hope this helps! Andy
