Question

Suppose 3 TAs will grade the final exam. Assume they are named Tı, T2, T3. The time it takes each of them to grade an exam is an exponential random variable, but with different parameters: the TA Ti grades the exams at a rate oft exams an hour Assume that the time to grade any exam is independent of the time to grade the other exams. Each exam is assigned to a uniformly random TA (a) (5 points) If X is the time it takes to grade your exam, compute E[X] and Var [X]. (b) (10 points) You find out that it took more than an hour to grade your exam What is the probability that it was the TA T2 that graded your exam?

Answer 1

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