But the web doesn't talk about these measures relationship with probability. Like what do they mean when it comes to a distribution of a random variable. (E.g: X~N(1,0) , 0 = stdev, 1 = mean)
@Delta, You must tell more about yourself and the course in which you are enrolled.
The main thing about your course because your questions imply that the answers require calculus based, set theory based concepts.
Most theoretical based probability courses begin with
Probability Spaces
Probability Spaces
Given any collection of objects, \(\displaystyle S\), there is a function, \(\displaystyle \mathcal{P}\) which maps the power set, \(\displaystyle \mathscr{P}(S)\) of )[the set of all subsets of which are called events] to the number interval \(\displaystyle [0,1]\) . The function, \(\displaystyle \mathit{P}\) called the probability measure on has three rules:
1) If \(\displaystyle A\subseteq S\) then \(\displaystyle 0\le \mathcal{P}(A)\le 1\)
2) \(\displaystyle \mathcal{P}(S)=1\)
3) If \(\displaystyle \{A,B\}\subseteq\mathscr{P}(S)\) and \(\displaystyle A\cap B=\emptyset\) then \(\displaystyle \mathcal{P}(A\cup B)=\mathcal{P}(A)+\mathcal{P}(B)\)
Those are the general concepts. But then there are three kinds of probability spaces:
finite, infinite discrete and continuous.
So tell us about your situation.
