The bird always eats for 4 h per day and spends 10 h sleeping when the weather is nice, 14 h sleeping when the weather is OK, and 18 h sleeping when the weather is bad. Find pS,P. Why are pE,P and pE,S not worth finding?
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.