When the weather is nice, the bird eats for 1 h and sleeps for 10 h. When the weather is OK, the bird eats for 1 h and sleeps for 14 h. When the weather is bad, the bird eats for 6 h and sleeps for 18 h. Find pS,P. Why is the correlation not perfect?
Consider birds that spend all of their time sleeping, eating, or preening. Let S be the time spent sleeping, E the time spent eating, and P be the time spent preening. How much time is spent on each activity depends on the weather, which is nice with probability 0.7, OK with probability 0.2, and terrible with probability 0.1.