1. (a) Define a random variable. Suppose you flip a coin once.' Give an example of a random variable for this experiment and show that it is a random variable b) Suppose the Canadian economy is equally likely to have an expansion, E, or a recession, R, in each of the following two years. Find ?, the sample space for this "experiment", and F, the set of all subsets of !?. (e) Let the random variable X' = {number of expansions) in (b). Find F., the e-algebra generated by X, and show that A' is a random variable. (d) Find the of and the pmf of X". (e) Let the random variable )' = {at least one expansion) in (b). Find F, the o-algebra generated by Y'. Is F, a subset of F