Confused by the notation in DAG depicting structural causal model and corresponding functional equations Statistical Notations confuses me a lot and I get lost easily in following when the authors are talking about random variables vs observations, probabilities, probability density functions or distributions etc.
Anyway in Pearl's "Causal Inference in Statistics: An Overview" (2009) I understood the following DAG to depict the causal relationship between Random Variables Z, X and Y.

but the corresponding non parametric functional equations are using small lower case letters:
$$
z = f_Z(u_Z)
$$
$$
x = f_X(z,u_X)
$$
$$
y = f_Y(x,u_Y)
$$
I interpret this that the lowercase letter represent an observation of the Random Variables. Is that assumption correct? How am I supposed to interpret the subscript for $f$ and $u$?

Yes, you are correct about upper-case versus lower-case: the upper-case $U_X,$ for example, is the exogenous random variable. Any particular value of that random variable is $u_X.$ This is a fairly common statistical notation practice: the upper-case is the random variable, the lower-case a particular value of that random variable.
The subscripts for $f$ and $u$ are there simply to distinguish them: it is not the case that the form of the functions for $x, y,$ and $z$ are all the same, nor is it the case that the exogenous variables $U_X, U_Y,$ and $U_Z$ are all identical; far from it, we usually assume the exogenous variables are independent, though there are ways to handle dependence.
