A resource I used when learning random signals was Proof Wiki (http://www.proofwiki.org/wiki/Main_Page). It has the proofs of many PDFs, CDFs, and PMFs, some of which were not covered in the textbook. Although the proving involved in the introductory random signal course was not hard, having Proof Wiki to compare the methods used to prove were still helpful (inspiring me somehow).
If checking the homepage, one might find that the theories included in Proof Wiki are not only the fundamental ones (ex. complex modulus) but also those more advanced ones (ex. central limit theorem), used in specific engineering and scientific fields.
I am thinking to contribute something, too, but so far, there have been many smart (or simply enthusiastic) people who have contributed the stuff I think of. Maybe some day I can catch up the giants' progress?
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