What if you have a PR3 site then you made a sub-domain, would the new sub-domain be also PR3? What about if the link is something like: http://yourdomain.com/forum is that rated differently from http://yourdomain.com ?
Every page of a website has its own PageRank. Technically, it is incorrect to say that one has a "PR4 website", because it is individual pages that have PR. The website as a whole is not given a PR. When people (incorrectly) say, "I have a PR4 website", what they actually mean in most cases is that they have a PR4 home page. For example, the home page of my website is PR5. Maybe 20% of the rest of the pages are PR4. The remaining pages (except the new ones that don't have PR yet) are PR3. In brief, no, the PR of your home page will not necessarily be the PR of any other pages. Each page will have its own PR, based on how each one scores in Google's extremely complex, secret algorithm.