2. (30) ECE 280 is taught each year by either Professor A or Professor B with equal probability. If Professor A teaches the class, then the exam grades, G are distributed as a Gaussian with mean 60 and standard deviation 5. If Professor B teaches the class, then the exam grades, Gare distributed as a Gaussian with mean 50 and standard deviation 20. (a) Sketch the two grade distribution pdfs for Professors A and B on the same plot. (b) What is the probability that a student gets a grade higher than 70 (G > 70) when Professor A is teaching the class? (c) If a student is aiming to get at least a 70 (G > 70) in this class, from which professor should the student take the class? (d) Given that a student gets a grade greater than TO, what is the probability that Professor B was teaching the class