Suppose the state of the economy in each quarter is an i.i.d process and is either good (G) with probability 0.4 , or not good with probability 0.6 . If the state is not good, it is either normal (M) or bad (B). Suppose further that you can only observe if the state is good (G) or not, and you cannot differentiate between M or B. The following tree depicts this economy: 1. What is the sample space of the possible states of the economy over the next two quarters? 2. For each date t=0,1,2, find the event space Ft that is composed of events that you can determine whether or not they have happened by that time. 3. Find the probability function Pt that tells you the probability that each event in Ft happens, t=0,1,2. 4. Suppose that there is a stock that pays a dividend dt at each time t, with d0=$0. The amount of dividend will depend on the state of the economy in the previous quarter. In particular, dt=$2$1$01ifthepreviousquarterwasGifthepreviousquarterwasMifthepreviousquarterwasB 1 (a) Find the common probability space (,F,P) on which d0,d1,d2 are random variables. If F is too big to write down, you can describe it in words. (Hint. The event space F consists of events that you can determine whether or not they have happened by observing d0,d1,d2 ). (b) Do you have enough information to find the probability function P of the above probability space