(3) The designers of a true-false test would like to find out how a student would perform if the student just guessed all the answers at random. (Designers of multiple-choice tests like the SAT have to consider this issue as well.) There are 200 questions on the test. 1 point is awarded for each correct answer and 1 point is taken away for any other kind of answer (wrong, missing, ambiguous, or anything other than correct). The test designers have figured out that the number of questions the student gets right by guessing at random has the expectation 100 and the standard deviation 10. (a) [1pt] Let W be the number of questions the student does not get right, and R be the number of questions the student gets right. Find a relation between W and R. (b) [1pt] What is EW? (c) [1pt] What is SD(W)? (d) [1pt] Let S be the student's score on the test. What is ES? (e) [1pt] What is SD(S)