3. In a large lecture course there are 3 exams. The scores on each of the...

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3. In a large lecture course there are 3 exams. The scores on each of the exams can be treated as random variables. Assume that the scores on exam 1, X₁, have a mean of 80 and a standard deviation of 10, the scores on exam 2, X2, have a mean of 75 and standard deviation of 15, and the scores on exam 3, X3, have a mean of 82 and standard deviation of 8. In the determination of the final grade, exams 1 counts 20%, exam 2 counts 30%, and exam 3 counts 50%. A student's grade is determined by the formula: grade = 0.2X₁ +0.3X2 +0.5X3 a. (2) Find the expected grade in the class at the end of the semester. b. (3) Assuming three exams are independent, find the standard deviation of "grade" at the end of the semester. c. (6) Now suppose exam 3 is independent of exam 1 and 2, but the correlation between exam 1 and 2 is 0.7. Would this change alter your answers to parts (a) and (b)? If so, how? 3. In a large lecture course there are 3 exams. The scores on each of the exams can be treated as random variables. Assume that the scores on exam 1, X₁, have a mean of 80 and a standard deviation of 10, the scores on exam 2, X2, have a mean of 75 and standard deviation of 15, and the scores on exam 3, X3, have a mean of 82 and standard deviation of 8. In the determination of the final grade, exams 1 counts 20%, exam 2 counts 30%, and exam 3 counts 50%. A student's grade is determined by the formula: grade = 0.2X₁ +0.3X2 +0.5X3 a. (2) Find the expected grade in the class at the end of the semester. b. (3) Assuming three exams are independent, find the standard deviation of "grade" at the end of the semester. c. (6) Now suppose exam 3 is independent of exam 1 and 2, but the correlation between exam 1 and 2 is 0.7. Would this change alter your answers to parts (a) and (b)? If so, how?

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a To find the expected grade in the class we need to calculate the expected value of the grade Given that each exam contributes a certain weight to th... View the full answer