Notation of random variables I am really confused about capitalization of variable names in statistics.
When should a random variable be presented by uppercase letter, and when lower case?
For a probability $P(X \leq x)$, what do $x$ and $X$ mean here?

An uppercase letter is usually for a random variables which is a function on events with a real number as its return value. A lowercase letter is for a realization of a random variable, which is a value. So $P(X<x)$ means the probability that the range of the function $X$ is less than the value $x$.
