I am bit confused when trying to connect the concept of realisations of "a" random variable or random variables to the real data observed for the analysis.
For example, the data observed are the measurements of total cholesterol level of 1000 patients, denoted $y_1$, $y_2$,...,$y_{1000}$.
My current understanding is that:
Each $y_i$ is a realisation from a single random variable $Y_i$ for $i^{th}$ patient such that $Y_i: \Omega([160, 300])\rightarrow R$. So there are 1000 random variables. The observed data are the realisations from these random variables.
In this case, we can talk about convergence of mean total cholesterol level by considering a sequence of random variables $\frac{1}{n}\sum^n_{i=1}{Y_i}$ when number of observations $n\rightarrow\infty$ .
- The distribution plot such as a histogram or a density plot is in the sense of empirical distribution. Since they are iid random variables, so the distribution from 1000 observations is the empirical distribution where each patient's total cholesterol could come from.
Would this be a proper understanding from an intuitive way?