An app is running on a computer initially, which may start other apps, which may in turn start other apps, and so on. During its runtime, each app will start a random number of other apps independently from the other apps with distribution POI(0.9).

(a) Let X_2 denote the number of apps started by an app started by the initial app. Calculate E(X_2) and P(X_2 = 0).

(b) What is the probability that eventually, no more apps will be started?

(c) Calculate the expected number of total apps started.