Question
Let N be a non-negative, integer-valued random variable, Show that
P{N > 0} >= (E[N])2/E[N ]2
And explain how this inequality can be used to derive additional bounds on a reliability function.
HINT: E[N ]2 = E[N 2|N > 0]P{N > 0} (Why?)
>= (E[N |N > 0])2P{N > 0} (Why?)
Now multiply both sides by P{N > 0}.