A Markov process on E = {1, 2} is constructed according to holding time parameters λ1 = 2 and λ2 = 4; the defining Markov chain has transition probabilities
p11 = p12 = 0.5
and
p21 = 1.
How do I calculate the generator matrix for this process?
Also what is the variance of the time (starting from state 1) until the process jumps to state 2?
EDIT USING: \begin{align} \nonumber g_{ij} = \left\{ \begin{array}{l l} \lambda_i p_{ij} & \quad \textrm{ if }i \neq j \\ & \quad \\ -\lambda_i(1-p_{ii}) & \quad \textrm{ if }i = j \end{array} \right. \end{align} I have calculated the generator matrix to be:
-1 1
4 -4
However I still have no clue how to solve the second part of the question,
Any help would be appreciated
what is the variance of the time (starting from state 1) until the process jumps to state 2?