A man finds that two things cause him to wake up at night- his cat or his dog. If it is due to his cat, the time to fall asleep again has exponential distribution with rate 5 per hour, and if it is due to his dog the time to fall asleep again has exponential distributin with rage 2 per hour. When he is asleep, he stays asleep for aan exponentially distributed time with mean 2 hours. Assuming the waking and sleeping periods are all independent of each other and that each time he wakes up it is due to his cat with probability 2/3 and due to his dog with probability 1/3. Draw rate diagram and set up balance equations.
A) what proportion of the time is he up because of his dog?
B) What proportion of the time does he actually spend sleeping