Continuation. In the context of Exercise 10, let X(t) denote the type of job being processed at time t. Find the limiting distribution of X(t). Find the portion of time devoted to type i jobs.Exercise...

Continuation. In the context of Exercise 10, let X(t) denote the type of job being processed at time t. Find the limiting distribution of X(t). Find the portion of time devoted to type i jobs.Exercise 10Partitioning and Thinning of a Renewal Process. Let N(t) be a renewal process with inter-renewal distribution F. Suppose each renewal time is independently assigned to be a type i renewal with probability pi, for i = 1,...,m, where p1 + ··· + pm = 1. Let Ni(t) denote the number of type i renewals up to time t. These processes form a partition of N(t) in