Forgive me beforehand for what may be a question with an obvious seolution, but I havent had statistics courses in quite some time.
I have an Excel File of approximately 3000 Events, each event has a numberdesignation attached to it (from 1-19). File looks like attached in the picture.
My question is concretely: How do i Calculate the Probability of a number occuring between two other numbers as displayed in the picture, the probability of "17" Occuring between two "18". Also how would i calculate the probability of number x occuring between two different numbers x1 and x2 such as number 14 occuring between 12 and 19.
https://i.stack.imgur.com/Rqjdh.png
So if anyone knows the name of the methodology/formulas i am looking for please let me know.
Thanks!
Without further assumptions, let $\Omega=\{1,\dots,19\}$. Let $X_i$ denote the value of the $i$-th experiment (or realisation). I guess assuming stationarity will still fit your problem.
If you are looking for $y\in\Omega$ between $x_1\in\Omega\backslash\{y\}$ and $x_2\in\Omega\backslash\{y\}$, by stationarity you can assume $X_0=x_1$ so you are looking for
$$\sum_{m=1}^{\infty}P(X_m = x_2, X_1,\dots,X_{m-1} \in \Omega\backslash\{x_2\}, \exists i\in\{1,\dots,m-1\}: X_i=y). $$
Depending on the distribution of your events you can simplify this.