Suppose N identical balls are distributed into two boxes. A ball in box A (box B) remains there for a negative exponential time parameter λ (parameter µ) and goes to the other box. The balls act independently. Let X(t) denote the number of balls in box A at time t. Then X(t) is a birth-and-death process defined over 0, \, ... , N.
(i) Find the birth and death rates.
(ii) Find PxN( t).
(iii) Find E( X(t).