Let N be a nonnegative, integer-valued random variable. Show that P{N > 0} (E[N])2 E[N2]

and explain how this inequality can be used to derive additional bounds on a reliability function.

Hint:

E[N2] = E[N2 | N > 0]P{N > 0} (Why?)

(E[N | N > 0])

2P{N > 0} (Why?)

Now multiply both sides by P{N > 0}.