In: Statistics and Probability
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.