If I pick a hosting package that offers CDN support, then how do server stat tools work, since web pages are served by different servers from all over the world?
Can I rely on them in that case?
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Generally with any server-side language in play, your webpages are going to be created by the server directly and won't be duplicated by the CDN.
Instead, a CDN is generally most effective when used on static assets like images, audio or video files, pdfs, word docs, etc. But most of all images, including the images in any page on the server. So you won't get the same stats simply for those static assets, but you'll get most page loads.
In general, I wouldn't worry too much about inaccuracies due to CDN usage, the various stats packages generally have some wiggle room in terms of what they can actually pick up accurately anyway.
And, of course, the benefits of a CDN are worth it if you get a speed boost out of it.