A student takes a test in which they have to indicate whether each of n statements is true or false. The student knows nothing at all about the subject matter and guesses the answers randomly. Let X denote the number of correct answers (a) Write down expressions for the expectation, E(X), and the variance, var(X). Suppose the student gets three marks for every correct answer but loses one mark for every incorrect answer. Let Y denote the student’s total score. (b) Show that Y = 4X −n. (c) Write down expressions for E(Y ) and var(Y ).

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