I'm new to ML/stats so got confused with what I supposed was simple notation.
For simplicity, say I have a data set with just one column:
From probabilistic perspective, I had understood that X represents a random variable, and each row value is an observation (i.e. realization) of this random variable. X then has a distribution, which let's assume is Gaussian.
I got confused however when I studied the Maximum Likelihood Estimate (MLE) method. In MLE literature, it's assumed that the individual row values are iid, which then permits us to multiply their distributions:
Isn't iid however a property of random variables? In other words seems MLE is assuming that each row value by itself is a random variable with its own distribution. Doesn't this contradict the previous interpretation that X is a random variable and the row values are just specific realizations?