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Question: A test consists of 10 true-false questions. Suppose a student answers the questions by flipping a coin. Let X denote the number of correctly answered questions.
(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 question.
(d) Let Y = 10 - X. In words, what does Y represent?
(e) Use the CDF to find P(2 ≤ Y ≤ 5).
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