Problem 4 Let X(t) be the birth-death process with birth rates li O and death rates Mi = u for some fixed u > 0. This process is known as the pure death process with death rate u > 0. Assume that the initial state is X(0) = N for some fixed positive integer N. Using Kolmogorov's backward equations, it can be shown that the transition probabilities Pi,j(t) = P(X(t) = j\X(0) = i) are determined for 0 0. This process is known as the pure death process with death rate u > 0. Assume that the initial state is X(0) = N for some fixed positive integer N. Using Kolmogorov's backward equations, it can be shown that the transition probabilities Pi,j(t) = P(X(t) = j\X(0) = i) are determined for 0