Answer Happy

Stochastic Data Processing
5. Lani is an undergraduate student whose health appears to be a continuous time Markov process uctuating between three states: 0 (t), 1 (minor illness which prevents him studying but does not stop him working at his part-time job), 2 (major illness requiring him to stay at home). When he develops an illness from the t state, it has a probability 3/4 to be a minor illness and a probability 1/4 to be a major illness. From a minor illness, he recovers with probability 2/3 or develops a major illness with probability 1/3. From a state of major illness, he always returns directly to full fitness. Assuming time units of days, the sojourn times in states 0,1,2 are exponentially distributed with parameters 1/4, 1/2, 1/6, respectively what is the long-run proportion of time Lani is able to study?