Each individual in a biological population is assumed to give birth at an exponential rate A and to die at an exponential rate |J. In addition, immigrations of single individuals occur according to a Poisson process with rate Q. The population size is a birth and death process. a. The birth rates are A; = for j;= 0,1,2,. .. b. The death rates are Hi: for j;= l,2,3,... Note that [Jo : 0. A birth and death process is a special case of a continuous-time Markov chain. Give the parameters for the continuoustime Markov chain. c. What is the rate associated with the state 1,? vi : for i;= 0,1,2\"; (1. From state i, i;= 0,1,2,.. ., we will either: transition to state with probability or transition to state with probability