1. Consider an urn which initially has m white balls and b black balls. Make a sequence of draws from the urn as follows. Draw one of the balls in the urn at random, then put this ball back into the um and add another ball to the urn of the same colour of the one just drawn. Continue to draw and add balls in this manner indenitely. Let Xn = 1 if the nth ball drawn is White and Xn = 0 if it is black. Let Yn be the number of white balls in this urn after the nth stage of the process. Thus, Y0 = w. (a) Is Y\" a Markov process? Notice that the total number of balls after nth stage is w + b + n (increasing in time). (b) If Y\" is Markov identify the state space and give its transition probability at time n. For this question we will allow the transition probabilities pn(1,j) to depend on the value of time n