Problem 1 Suppose the the economy in Example 1, Lecture 1 lasts for three quarters. Similar to Example 4 of Lecture 1, consider a security that pays dt = $1 if the economy state in quarter it is G and dt = $0 if the economy state in quarter 73 is B. Let X 2 d1 + d2 + d3. Let 3,75 = 1, 2,3 be the sigmaalgebra that describes the information at time t. 1. Calculate the conditional expectations Z = IE[X|J-'t] (note that Zt's are random variables themselves). 2. Find the Ualgebras generated by Z, t = 1, 2, 3