Statistics 103: Midterm 3 Test Form C (Dated: March 2, 2016) Instructions: Before you do anything, make sure your name, ID and your test form type is on your scantron. You have until 11:50am to finish this test. You may use one sheet of notes and a calculator. 1. Suppose X and Y are bivariate normal with correlation = 0.42. Predict the z-score for Y when observing the z-score of X to be 3.2. (a) 0.0 (b) 0.42 (c) 1.539 (d) 0.64638 (e) 1.344 Answer: 1e (b) 4.230 (d) 47.0 6. Suppose W and Q are bivariate normal random variables such that E(W ) = 1, sd(W ) = 10 E(Q) = 10, sd(Q) = 2 = 0.1. sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 2. Suppose X and Y are bivariate normal with correlation = 0.9. Predict the z-score for X when observing the z-score of Y to be 1.71. (a) 0.9 (b) 0.9 (c) 1.9 (d) 1.539 (e) 1.539 Answer: 2e (a) 4.846 (c) 4.0 (e) 0.7692 Answer: 5a 3. Suppose X and Y are bivariate normal and satisfy E(X) = 10, sd(X) = 15 E(Y ) = 5, sd(Y ) = 2 = 0.9. Predict Y when observing that X is at the 50th percentile. (a) 7 (b) 0 (c) 3 (d) 5 (e) 4.5 Answer: 3d 4. Suppose X and Y are bivariate normal random variables such that E(X) = 10, sd(X) = 15 E(Y ) = 5, sd(Y ) = 1 = 0.8 Th If you observe X = 25 then your best prediction for Y is 5.8. What is the typical prediction error associated with this prediction? (a) 1 (b) 0.8 (c) 0.6 (d) 0.64 (e) None of the above Answer: 4c 5. Let W and Q be two random variables such that E(W ) = 5, sd(W ) = 1 E(Q) = 110, sd(Q) = 52 = 0.2 Assume (W, Q) are bivariate normal. What is the expected value of W given Q = 150 https://www.coursehero.com/file/13990810/Midterm3Csolutionspdf/ Predict the value of Q when you observe W = 20. (a) 0.19 (c) 13.8 Answer: 6d (b) 6.0 (d) 10.38 7. Suppose X and Y are bivariate normal random variables such that E(X) = 10, sd(X) = 15 E(Y ) = 5, sd(Y ) = 1. Suppose E(Y |X = 25) = 5.8. correlation between X and Y . (a) 1.25 (b) 0.28 (c) 0.1724 (d) 0.8 (e) 1.0 Answer: 7d What is the 8. Suppose X and Y are bivariate normal random variables such that E(X) = 10, sd(X) = 15 E(Y ) = 5, sd(Y ) = 1 = 0.25 What is the predicted z-score of Y when observing 100X 200 = 2300. (a) 1.27 (b) 5.25 (c) 0.4557 (d) 0.25 (e) 0.18333 Answer: 8d 9. Let X and Y be two bivariate normal random variables such that E(X) = 5, sd(X) = 10 E(Y ) = 10, sd(Y ) = 2 = 0.5. 2 Find P r(X 0|Y = (a) 0.99999 (c) 0.074 (e) 0.1057 Answer: 9c 7). (b) 0.386 (d) 0.9255 10. Suppose X and Y are positively correlated bivariate normal random variables such that var(Y |X = x) = var(Y ) . 10 What is the correlation between X and Y ? (a) 0.9 (b) 0.948683 (c) 0.1 (d) 0.3162 Answer: 10b 12. Suppose you have a candy bar which weights 1.55 ounces. Your going to split it in two and share with your friend (you keep one part, your friend keeps the other). Unfortunately, it is nearly impossible to split a candy bar exactly in half since the break point is eectively random. Let X be the weight of your part and Y be the weight of your friends part. What is the correlation between X and Y (hint: draw a hypothetical scatter plot of X and Y ). (a) 0 (b) 1 (c) 1 Answer: 12c Th sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 11. Suppose X and Y are bivariate normal. Also suppose that when X is observed to be at the 10th percentile (among all possible X's) then the best prediction of Y is at the 90th percentile (among all possible Y 's). What is the correlation between X and Y ? (a) 1 (b) 1 (c) 0 (d) 0.92 (e) 0.92 Answer: 11a https://www.coursehero.com/file/13990810/Midterm3Csolutionspdf/ Powered by TCPDF (www.tcpdf.org)