Atest consists of 10 true-false questions. suppose a student answers the questions by flipping a coin, that is, if head means true and tail means false. let x denote the number correctly answered questions. (hint: it might be if you use relevant r commands to obtain the values of pmf and cdf.) (a) give the expected value and variance of x. (b) find the probability the student will answer correctly exactly 5 of the questions. (c) find the probability the student will answer correctly at most 5 of the questions. use the cdf to answer this quesition. (d) let y = 10 − x. in words, what does y represent? (e) use the cdf to find p(2 ≤ y ≤ 5).