2) An average of 40 children per hour, which are exponentially distributed, are arrived at the playground. If more than 2 children are in the line for the swing (2 in the line+2 on the swing). the new child will not enter the line. There are only two swing seats, so only two children can swing at a time. Child's swing times are exponentially distributed with mean 6 minutes.

(a) Define state, and state space, and draw a rate diagram 

(b) What is the average number of children waiting for the swing? (not including the child swinging on the swing)

(c) On average, how many children will be swing per hour?