A grade in a probability course depends on exam scores X1 and X2. The professor, a fan of probability, releases exam scores in a normalized fashion such that X1 and X2 are independent Gaussian (μ = 0, σ = √2) random variables. The semester average is X = 0.5(X1 + X2). 1. A student was to earn an A grade if X > 1. What is P(A)? 2. To improve the RS (Rating Service) score, the professor decides he should award more A’s. Now you get an A if max(X1, X2) > 1. What is P(A) now? 3. The professor found out he is unpopular and decides to award an A if either X > 1 or max(X1, X2) > 1. Now what is P(A)? 4. Under criticism of grade inflation from the department chair, the professor adopts a new policy. An A is awarded if max(X1, X2) > 1 and min(X1, X2) > 0. Now what is P(A)?
A grade in a probability course depends on exam scores X1 and X2. The professor, a
fan of probability, releases exam scores in a normalized fashion such that X1 and X2 are independent
Gaussian (μ = 0, σ = √2) random variables. The semester average is X = 0.5(X1 + X2).
1. A student was to earn an A grade if X > 1. What is P(A)?
2. To improve the RS (Rating Service) score, the professor decides he should award more A’s. Now you get an A if max(X1, X2) > 1. What is P(A) now?
3. The professor found out he is unpopular and decides to award an A if either X > 1 or max(X1, X2) > 1. Now what is P(A)?
4. Under criticism of grade inflation from the department chair, the professor adopts a new policy. An A is awarded if max(X1, X2) > 1 and min(X1, X2) > 0. Now what is P(A)?
Detailed explanation and calculation would be much appreciated.
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