Align a cases equation with another equation vertically on the same line

I am using the following to align the two equations. However, they are not vertically on the same level. How should I fix it?

\documentclass{article}

\usepackage{amsmath}

\begin{document}
\begin{equation*}
\begin{split}
G(Q,N)=\sum\limits_{Q_i \in N} F(Q_i,N); \;\;
\end{split}
\begin{split}
F(n,N)=
\begin{cases}
1, & \text{if } n > N \\
0.5, & \text{if } n = N \\
0, & \text{otherwise}
\end{cases}
\end{split}
\end{equation*}
\end{document}


Don't set each part in a split. Instead, just separate them with a \qquad (or some other horizontal space). This ensures that the math axis is not adjusted.
\documentclass{article}
$G(Q,N) = \sum\limits_{Q_i \in N} F(Q_i,N); \qquad F(n,N) = \begin{cases} 1, & \text{if } n > N \\ 0.5, & \text{if } n = N \\ 0, & \text{otherwise} \end{cases}$