Suppose that the number \(N_{t}\) of salmon that have passed a point on a river by time \(t\) forms a Poisson process with rate 2 per minute. The probability is \(1 / 4\) that a given salmon is over five pounds, and successive salmon weights are independent of one another. Show that the arrival process that counts only the number of salmon exceeding five pounds is also Poisson, and find its rate.