Let the price of one share of a stock be represented by a stochastic process X={Xt : t{0,1,2,3,4}}. Consider the following possible realizations for the stochastic process Figure 1. Realizations of a stochastic process (1) What -algebras (F0,F1,F2) are generated by random variables X0,X1, and X2 ? (2) What is the conditional distribution of X4 if you know X2 ? (3) Calculate the conditional expectation of X4 if you know X2. (4) This exercise explains why filtration F0F1F2 is called information. Assume t=1. List some events from F2 occurence of which you currently cannot determine. Let the price of one share of a stock be represented by a stochastic process X={Xt : t{0,1,2,3,4}}. Consider the following possible realizations for the stochastic process Figure 1. Realizations of a stochastic process (1) What -algebras (F0,F1,F2) are generated by random variables X0,X1, and X2 ? (2) What is the conditional distribution of X4 if you know X2 ? (3) Calculate the conditional expectation of X4 if you know X2. (4) This exercise explains why filtration F0F1F2 is called information. Assume t=1. List some events from F2 occurence of which you currently cannot determine