Answer Happy

Sample mean. We wish to estimate the approval rating of a president, to be called B. To this end, we ask n persons drawn at random from the voter population for their approval/disapproval voting. Let X, be a random variable that encodes the response of the yeh person: 1, if the oth person approves B's performance if the ith person disapproves B's performance We model Xs as i.i.d Bernoulli random variables with mean p. The sample means is defined x-{: X as x + X₂+...+x, S. n a. Find the mean of S. b. Find the variance of S, c. How large should n be such that. P{Sn-pl > 0.01} <0.1? Find such n using the Chebyshev inequality Note: we are not given the numerical value p, which means we can not determine the variance of Xis. However, we know that the variance of Xis is at most 1/4 as Var( X) = p(1-P) can take values between 0 and 1/4.