Probability & Stochastic Proc

Q3

[15 marks] At time 0, a blood culture starts with X0 = 1 red cell. At the end of 1 minute, the red cell dies with probability 1/5, or with probability 4/5 the red cell splits into two cells, with each of them being a red cell with probability p E (0, 1) or a white cell with probability 1 p. Each red cell lives for 1 minute and dies or divides in the same way as the parent cell. Each white cell lives for 1 min and dies without reproducing. Each individual cell behaves independently of the other. . oo oo 00 ask (Him: for |m|