[Tex/LaTex] Big curly braces Inside the equation

Question

I am trying to print following following equation in latex

The code I have

\documentclass{article}   
\usepackage{amsmath, amsthm, amssymb}
\begin{document}
\begin{equation}
  P(Z_{n+1}=T|Z,Z_{1}\dots Z_{n}; \alpha) =
    \begin{cases}
       c(n) = \frac{\alpha}{n} & \text{for }1\le i<l\\
            \\
    \end{cases}
\end{equation}
\end{document}

The code doesn't produce the required output.

Produced result.

Answer 1

Something like the following? (Observe that \mid gives better spacing than | does.)

\documentclass{article}   
\usepackage{amsmath}
\begin{document}
  \begin{equation}
   P(z_{n+1}=t \mid z_{1},\dots ,z_{n}; \alpha) = 
  \begin{cases}
     \frac{n_t}{n+\alpha} & \text{if table $t$ is occupied}\\
     \frac{\alpha}{n+\alpha} & \text{if table $t$ is empty}
  \end{cases}
  \end{equation}
\end{document}