(7) There are 14 small balls of the same size and shape, 7 of which are red and 7 are white. They are placed in two boxes, A and B, where box A contains 4 red balls and 3 white balls, and box B contains 3 red balls and 4 white balls. Now, a ball is randomly drawn from box A and placed into box B, then a ball is randomly drawn from box B and placed back into box A. Let the number of red balls in box B at this point be $\xi$, then the mathematical expectation $E \xi=$ $\qquad$.
(7) $\frac{25}{8}$ Hint: According to the problem, the values of $\xi$ are $2, 3, 4$.
$P(\xi=2)=\frac{3}{7} \times \frac{3}{8}=\frac{9}{56}$ (corresponding to the ball drawing situation of white $\rightarrow$ red);
$P(\xi=4)=\frac{4}{7} \times \frac{4}{8}=\frac{16}{56}$ (corresponding to the ball drawing situation of red $\rightarrow$ white); $P(\xi=3)=1-\frac{9}{56}-\frac{16}{56}=\frac{31}{56}$.
Therefore, the distribution of $\xi$ is
\begin{tabular}{|c|c|c|c|}
\hline$\xi$ & 2 & 3 & 4 \\
\hline$P$ & $\frac{9}{56}$ & $\frac{31}{56}$ & $\frac{2}{7}$ \\
\hline
\end{tabular}

Therefore, $E \xi=2 \times \frac{9}{56}+3 \times \frac{31}{56}+4 \times \frac{2}{7}=\frac{25}{8}$.