A class contains 30 students. The probability of failing in one of the courses for each student is 0.03, but there is no chance to fail in more than one course. You know that a student failed in a course, the probability that the fail reason in non-attendance is 0.01. All other fail reasons are low average. The examinations are private, so the results are mutually independent.

Let X and Y be the numbers of failed students due to non-attendance and due to low average, respectively, in that class this semester.

Find the joint MGF