1. Expectations: Suppose that at time time tEv the expected value of a random variable a is 0.05. Moreover, you observe realizations of 71' in subsequent periods till time t: 73-55 Z 0.04; ill-t_4 : 003-, Til-3-3 Z 002; g_2 Z 0.01; 5_1 Z 0.10. (a) What is the expected value of 71' at time t under adaptive expectations with A : 1 [i.e., static expectations)? (b) What is the expected value of 7:" at time t under adaptive expectations with A 2 i? (c) What is the expected value of 71' at time t under type 1 expectations? (Hint: Suppose t z 10) (d) What is the expected value of 11' at time t under rational expectations? Can you actually derive it? Why yes/ no? Explain