6.7 Consider a Markov renewal process with the semi-Markov kernel Q given by Q 5 0:61 2 e25t 0:41 2 e22t 0:5 2

6.7 Consider a Markov renewal process with the semi-Markov kernel Q given by Q 5 0:6ð1 2 e25t Þ 0:4ð1 2 e22t Þ 0:5 2 0:2 e23t 2 0:3 e25t 0:5 2 0:5 e22t 2 t e22t " #

a. Determine the state-transition probability matrix P for the Markov chain fXng.

b. Determine the conditional distributions GijðtÞ of the waiting time in state i given that the next state is j for all i, j.