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Problem 21.54. In an exam with n questions, let p be the probability a student answers question i correctly. (a) What is the condition

Problem 21.54. In an exam with n questions, let p be the probability a student answers question i correctly. (a) What is the condition on the p so that the expected grade on the exam is 80%? (b) Show that the grade-variance is maximized when pi = 0.8 (this helps to better differentiate students).

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