Here's the revised version of your code
Code:
<IfModule mod_expires.c>
ExpiresActive on
# Set expiration for HTML files
ExpiresByType text/html "access plus 10 minutes"
# Set expiration for favicon
ExpiresByType image/x-icon "access plus 1 month"
# Set expiration for image files
ExpiresByType image/gif "access plus 1 month"
ExpiresByType image/png "access plus 1 month"
ExpiresByType image/jpg "access plus 1 month"
ExpiresByType image/jpeg "access plus 1 month"
# Set expiration for CSS and JavaScript files
ExpiresByType text/css "access plus 1 week"
ExpiresByType text/javascript "access plus 1 week"
# Configure Cache-Control and Vary header
<IfModule mod_headers.c>
Header append Cache-Control "private"
<FilesMatch "\.(js|css|gz)$">
Header append Vary "Accept-Encoding"
</FilesMatch>
</IfModule>
</IfModule>