"* Roger John Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences, [lecture notes](https://arxiv.org/pdf/1905.12362.pdf)\n",
"<br>\n",
"\n",
"* Volker Blobel, Erich Lohrmann, Statistische und numerische Methoden der Datenanalyse,[pdf](https://www.desy.de/~sschmitt/blobel/eBuch.pdf)\n",
* Roger John Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences, [lecture notes](https://arxiv.org/pdf/1905.12362.pdf)
<br>
* Volker Blobel, Erich Lohrmann, Statistische und numerische Methoden der Datenanalyse,[pdf](https://www.desy.de/~sschmitt/blobel/eBuch.pdf)
%% Cell type:markdown id:a3347273 tags:
## Probability
### Probability
When is a system *random*?
The degree of randomness can a quantified with the concept of *probability*.
Consider the sample space $S$:
Axioms by Kolmogorov:
- for every subset $A$ in $S$,
$P(A) \ge 0$
- for two disjoint subsets $A$ and $B$
($A \cap B = \emptyset$),
$P(A \cup B) = P(A) + P(B)$
- for the whole sample space $S$,
$P(S) = 1$
*random variable*: a variable that takes on a specific value for each element of $S$
%% Cell type:markdown id:a7de85eb tags:
### Conditional probability
%% Cell type:markdown id:67a031e2 tags:
Definition: **Conditional probability**
Conditional probability for two subsets $A$ and $B$ in $S$:
$P(A|B) = \dfrac{P(A \cap B)}{P(B)}$
Definition: **independence**
Two subsets $A$ and $B$ in $S$ are independent, if