Miscellanous things to remember

1. Sorry for my laziness....
I have faced A/B/C type of unit while studying enigneering. However, sorry for myself, I have not given thought what is equivalent for conventional division form.
Here is ...the answer.
A/B/C = (A/B)/C...keep diving previous terms.

ex) 100 photons/label/sec = 100 (photons/label)/sec = 100 photons/(label x sec)

2. Relationship between independet and uncorelated
Assume that random variables X and Y,
We all know that...

X and Y are "independent" --> joint probability mass function (PMF) for discrete RVs or joint probability density function (PDF) for continous RVs can be represented as each marginal PMF/PDF.

X and Y are "uncorrelated" --> Covariance X and Y: Cov[X,Y] = 0

Since X and Y are independent, then their covariance is zero. However, the reverse action is not neccessaril true. Thus, "independent" is a subset of "uncorrelated".

In engineering, particularily for noise power calculation, if two noise sources are uncorrelated or independent processes, each noise power can be added!!!

(note) Orthogonal RVs
X and Y are orthogonal --> zero correlation = E[XY] = 0!!
Thus, if X and Y are independent and one of (or both) process is zero-mean, then two processes are orthogonal!!!

...the end!