# sdu

posted by
**Anonymous**
.

. A man finds that two things cause him to wake up at night-noise or indigestion. If it is due to noise, the time to fall asleep again has exponential distribution with rate 5 per hour, and if it is due to indigestion the time to fall asleep again has exponential distribution with rate 2 per hour . When he is asleep, he stays asleep for an exponentially distributed time with mean 2 hours. Assuming the waking and sleeping perids are all independent of each other and that each time he wakes up it is due to noise with probability 2/3 and indigestion with probability 1/3, what proportion of time is he up because of indigestion and spend s ofn sleeping?