In Queueing Theory, is the Second Moment of service time the same as "Variance". I was given a homework question that has 3 parts -
(a) Service time exponentially distributed with rate $\frac15$,
(b) Deterministic service time equal to $5$,
(c) Service Time of equal probability of $1$ or $9$.
If we do the math, all (a), (b) and (c) have the same average service time. As such, I need to use Variance to differentiate them when using the Pollaczek-Khinchin (P-K formula).
Before doing so, I need to know if Variance is the same as Second Moment.
Any help would be great. Thanks.
Both are defined in queuing theory like in any field (I know or ever heard of) using probabilities. Given a random variable $X$
the variance is defined as $\mathbb{E}((X-\mathbb{E}(X))^2)$
the second moment is defined as $\mathbb{E}(X^2)$