Can anyone explain the syntax from the following Wikipedia article on the convergence of random variables?
In particular:
- What is the squiggly line?
- What are $d$, $D$, $L$, $L_X$?
- Why does it say $X_n$ implies X? They don't seem to be statements
Can anyone explain the syntax from the following Wikipedia article on the convergence of random variables?
In particular:
All of these expressions are just notations for "X_n converges to $X$ in distribution".
The squiggly line is really just a notation (a rather strange one) for convergence in distribution.
The symbols $d$ and $\mathcal D$ stand for distribution, $\mathcal L$ and $\mathcal L_X$ stand for law. (One also speaks of "convergence in law" instead of "convergence in distribution".
This is also just a notation for convergence in distribution (also a rather strange one); the arrow does not symbolize an implication of statements.