6.1.3 A population of organisms evolves as follows. Each organism exists, independent of the other organisms, for an exponentially distributed length of time with parameter , and then splits into two new organisms, each of which exists, independent of the other organisms, for an exponentially distributed length of time with parameter , and then splits into two new organisms, and so on. Let X.t/

denote the number of organisms existing at time t. Show that X.t/ is a Yule process.