Suppose you win $1 if a fair coin shows a head and lose $1 if it shows a tail. Denote the outcome on toss t by e (i.e., for toss t, & is either $1 or -$1 with 50% chance respectively). For each independent coin toss t, your average winnings on the last four tosses (wit) are 1/46 + 1/46t_1 + 1/46 2 + 1/4et-3 (1) (a) Find the expected value and variance of et. (b) Find the expected value of wt. Find the expected value given that (t-3 = ft-2 = 1. (c) Find var(w;). Find var(w;) conditional on 6 3 = ( 2 = 1. (d) Find: (i) Cov(wt, wt-1); (ii) Cou(wt, wt 2); (iii) Cou(wt, wt 5)