Suppose there are 2 states at date 1. State 1 takes place with probability 0.4 and state 2 takes place with probability 0.6. Suppose there are two securities, A and B that have the following payoff structures: security A has a payoff of 3 in state 1 and 2 in state 2, while security B has a payoff of 1 in state 1 and 2 in state 2. The price of security A is 2, and that of security B is 1.5. Now answer the following questions: a. What should be the risk neutral probability of state 1? b. What should be the risk free rate? c. Suppose there is another security C, which has a payoff of 1 in state 1 and 0 in state 2. Derive the price of this security using linear pricing rule. d. Describe how we can replicate the payoff of security C by using security A and B.