Consider a binomial tree model with S(0) = 10, u = 0.1, d = 0.2 and r = 0. Let P(2) be the payoff at time 2 of a put option with strike price 8. Determine the following conditional expectations under the risk-neutral probability: (a) E[P(2)|S(1)]

(b) E[(S(2))2 |S(1)]

(c) E[min{S(1), S(2)}|S(1)]