A professor has a quiz with two questions. Assume that the probability of answering question 1...

A professor has a quiz with two questions. Assume that the probability of answering question 1 correctly is x, the probability of answering question 2 is y, and the two questions are independent. Let S be the number of questions that a student will get correct (so S=0, 1, or 2). The professor wishes to choose x and y to maximize V(S) subject to E(S)=1.4 (70% of 2 questions). Find x and y using the definitions of expected value and variance, and the method of Lagrange Multipliers.

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A pop quiz has two questions. Question 1 is a multiple choice question with 4 possible...

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