Question

Suppose you win $1 if a unfair coin shows a head and lose $1 if it shows a tail. Denote the outcome on toss t by st. For each coin toss, there is 60% probability to get a head, and 40% probability to get a tail. For each independent coin toss t, your average winnings on the last three tosses (wt) are 1/3st + 1/3st−1 + 1/3st−2 (1) (a)Compute the expected value and variance of st. (b)(i) Compute the expected value of wt. (ii) Compute the expected value given that st−2 = 1. (c)(i) Compute var(wt). (ii) Compute var(wt) conditional on st−2 = 1. (d)Compute: (i) Cov(wt, wt−1); (ii) Cov(wt, wt−5).

Answer 1