question is attached, table one is the last picture c

3. (24 points) The following question is based on Table 1. It is based on a survey in which people were asked if they support President Trump and the same people were asked if they have a college degree. Suppose we randomly choose a person who participated in the survey. a Let T = 1 if the person approves of Trump and 0 if not. a Let C = 1 if the person has a college degree and 0 if not. (a) Find EH] (b) Find E[T|C =1] (c) Find E[T x C'] (d) What is the covariance of T and C? 4. (30 points) A statistics exam has ve easy questions and three hard questions. You have six friends who are in the class, ve are moderately prepared and one is very prepared. Probability Hard Questions Correct 66.666% (two-thirds) 80% Probability Easy Questions Correct 80% Chance 5 Moderately Prepared Friends 1 Very Prepared Friend The probability of answering any one question correctly is completely independent of the probability of answering any other question correctly for every student. (a) What is the probability your very prepared friend gets all eight questions right? (b) What is the probability that a randomly chosen moderately prepared friend gets all eight of them correct? (c) The professor randomly chooses one exam to grade rst. The exam happens to belong to one of your six friends and it happens to get all eight questions correct. What is the probability it is the exam of your one very prepared friend. (d) Let the random variable VP be the number of questions answered correctly by your very prepared friend. Find E[VP] (e) Let M1, M2, . . . , M5 be the scores received by your ve moderately prepared friends. Let D be the difference between the average score of your ve moderately prepared friends and the score of your one very prepared friend: M1+M2+M3+M4+M5 5 Find the variance of D (hint: Var-(VP) = .7175 and VGT(M{) = 1.4667) D= VP Table 1: Gallup Polling Data in 2017 on Trump Approval and Level of Education Have a College Degree? Approve of Trump's Job as President No Yes Yes 26.06% 16.66% No 28.08% 29.20%