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I'm looking for the right notation for features from different types. Let us say that my samples as $m$ features that can be modeled with $X_1,...,X_m$. The features Don't share the same distribution (i.e. some categorical, some numerical, etc.). Therefore, while $X_i$ might be a continuous random variable, $X_j$ could be a discrete random variable.

Now, given a data sample $x=(x_1,...,x_m)$, I want to talk about the probability, for example, $P(X_k=x_k)<c$. But $X_k$ might be a continuous variable (i.e. the height of a person). Therefore, $P(X_k=x_k)$ will always be zero. However, it can also be a discrete variable (i.e. categorical feature or number of kids).

I'm looking for a notation that is equivalent to $P(X_k=x_k)$ but can work for both continuous and discrete random variables.

To my knowledge, if $X$ is a continuous variable then for each constant $c$, $P(X=c)=0$. Instead of constants, we should talk about intervals and measure the probability using a probability density function. – Yael M – 2020-05-27T11:46:43.813