please solve this question step by step

2. Consider a birth and death process (X.0 51 0 and death rate 8 > 0. Denote by 6. = inf{1 20:X; = 0) the extinction time. (a) i) Recall the definition of the (8,6)-birth and death process as a population model and gives its diagram as a continuous-time Markov chain. ii) Using a property of this population model, show that! P,(6. 0? ii) Argue that 0 0. Show that pl Bp G(y) + = G(0), Vy 20 k! where p = v) Consider 8 > B and let us admit that F(I)