Two different professors have just submitted final exams forduplication. let x denote the number of typographical errorson the first professor%u2019s exam and y denote the number ofsuch errors on the second exam. suppose x has a poissondistribution with parameter \(\mu_{1}\) , y has a poisson distributionwith parameter \(\mu_{2}\) , and x and y are independent. a. what is the joint pmf of x and y? b. what is the probability that at most one error is made onboth exams combined? c. obtain a general expression for the probability that thetotal number of errors in the two exams is m (where m isa nonnegative integer). [hint: a {(x, y): x +y =m} ={(m, 0), (m -1, 1), . . , (1, m -1), (0, m)}. nowsum the joint pmf over (x, y) \(\epsilon\) a and use the binomialtheorem, which says that \(\sum_{k=0}^{m}(^{n}_{k})a^{k}b^{m -k} = (a+b)^{m}\) for any a, b.