Let X be a Poisson random variable with parameter λ. Show that the PMF pX(k) increases monotonically with k up to the point where k reaches the largest integer not exceeding λ, and after that point decreases monotonically with k.

Three students, javier, sam, and corrine, participated in a fundraiser where people donated a certain amount of money per lap that the student ran. each student also had some initial donations that were collected before the run. the equations that represent each student's total donation, y, based on the number of laps ran, x, is shown below. match each equation with the correct rate of change for that student.