# Reliability Theory Questions

These questions are a part of a Operations Research class with a section on Reliability Theory.

(See attached file for full problem description with proper symbols and equations)

---

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}.

---

https://brainmass.com/math/linear-programming/reliability-theory-questions-56151

#### Solution Preview

Please see the attached file.

Question

Let N be a non-negative, integer-valued random variable, Show that

P{N > 0} >= (E[N])2

E[N ]2

If X is a discrete random variable with ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer reliability theory questions. Non-negative, integer-values for random variables are examined.