Problem with simple TikZ plot

Question

I'm trying to make an explanatory graph that boils down to annotating curves between two arbitrarily placed points.

My TikZ/Tex code just isn't compiling even though it closely follows the manual; What am I doing wrong?

\documentclass{minimal}

\usepackage{tikz}
\usetikzlibrary{arrows,backgrounds,snakes,shapes}
\begin{document}

 \begin{centering}
  \begin{tikzpicture}[domain=0:4] 
   \draw[->] (-0.2,0) -- (4.2,0) node[right] {$\mu$}; 
   \draw[->] (0,-1.2) -- (0,4.2) node[above] {$\sigma$};
   \fill[color=red] (1,1) circle (1ex) {$a$}; 
   \fill[color=blue]  (2,3) circle (1ex) {$b$};
   \draw[->,color=black] (1,1) -- (2,3) node[right] {$ds_{ab}^2= 2KL$};
  \end{tikzpicture}
 \end{centering}
 \end{document}

Answer 1

The problem arises along the lines:

\fill[color=red] (1,1) circle (1ex) {$a$}; 
\fill[color=blue]  (2,3) circle (1ex) {$b$};

because here is not clear if you want to declare a node or just a circle. To make your document compile you have two solutions:

\documentclass{article} % first solution

\usepackage{tikz}

\begin{document}
 \begin{centering}
  \begin{tikzpicture}[domain=0:4] 
   \draw[->] (-0.2,0) -- (4.2,0) node[right] {$\mu$}; 
   \draw[->] (0,-1.2) -- (0,4.2) node[above] {$\sigma$};
   \fill[color=red] (1,1) circle (1ex); 
   \fill[color=blue]  (2,3) circle (1ex);
   \draw[->,color=black] (1,1) -- (2,3) node[right] {$ds_{ab}^2= 2KL$};
  \end{tikzpicture}
 \end{centering}
\end{document}

or

\documentclass{article} % second solution

\usepackage{tikz}

\begin{document}
 \begin{centering}
  \begin{tikzpicture}[domain=0:4] 
   \draw[->] (-0.2,0) -- (4.2,0) node[right] {$\mu$}; 
   \draw[->] (0,-1.2) -- (0,4.2) node[above] {$\sigma$};
   \fill[color=red] (1,1) circle (1ex) node{$a$}; 
   \fill[color=blue]  (2,3) circle (1ex) node{$b$};
   \draw[->,color=black] (1,1) -- (2,3) node[right] {$ds_{ab}^2= 2KL$};
  \end{tikzpicture}
 \end{centering}
\end{document}

If the purpose is to insert a label inside circles I suggest to proceed as follows:

\documentclass{article}

\usepackage{tikz}

\begin{document}
 \begin{centering}
  \begin{tikzpicture}[->,domain=0:4] 
   \draw (-0.2,0) -- (4.2,0) node[right] {$\mu$}; 
   \draw (0,-1.2) -- (0,4.2) node[above] {$\sigma$};
   \node[circle, radius=1ex,fill=red,text=black] (a) at (1,1) {$a$}; 
   \node[circle, radius=1ex,fill=blue,text=black] (b) at  (2,3) {$b$};
   \draw[color=black] (a) -- (b) node[right=0.2cm] {$ds_{ab}^2= 2KL$};
  \end{tikzpicture}
 \end{centering}
\end{document}

which gives:

Notice that I shift the option -> because it is common to every \draw then to connect the two nodes, first labels were assigned when they have been declared. Using the node declaration for a and b rather than your \fill allows the arrow to not overrides the circle. Indeed, the first solution above reported would lead to:

A final annotation: the snakes library is outdated; you should load decorations, but for this specific drawing it isn't necessary, as the other ones, see my examples.