Can you please provide a detailed explanation?

(10 points) Suppose I give a final project to a course that contains a very large number of students. Suppose that I have two Teaching Assistants to grade these final projects. Suppose the number of errors in grading per project made by the first TA has a Poisson distribution with mean value # and the number of errors in grading per project made by the second TA has a Poisson distribution with mean value /2. If each TA takes an equal share of the final projets to grade then it is reasonable that the function P(X = r) = .5 + .5 r! gives the probability of of a randomly selected final project having r grading errors. (a) Show that this is a legitimate probability mass function. (2 points) (b) What is the expected number of grading errors? (3 points) (c) What is the variance of the number of grading errors? (4 points) (d) How might the given function change if the first TA was able to grade 75% of the final projects? (1 point)