(a) A branching process has Bernoulli offspring distribution with parameter, =1/4 Let P(s) and Qn(s) be the probability generating functions of offspring distribution and total progeny up to n- th generation respectively. The two generating functions have the relation Qn(s)=sP(Qn1(s)). Find (i) the expected time to extinction. (7 marks) (ii) Find Q(s)=nlimQn(s) and hence the probability distribution of the total progeny . (4 marks).