A professor assigns 5 homework problems. The class has 3 TAs. For the entire class of 140 students, each problem requires an average of 2 hours to grade by each TA. The grading time for each problem by each TA is exponentially distributed, and both the problems and TAs are independent of each other. What is the probability that the TAs finish grading in a total of 10 hours?
Assuming that the TAs all work in parallel, starting at the same time, what is the probability that they finish grading in 3 hours?
Again, assuming the TAs work in parallel and start at the same time, what is the expected number of problems graded after 2 hours?
TA is the teaching assistant