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}.