Watch this lecture, in which Professor Stark works through several examples of probability distributions. The second video gives more information on how to find the mean (or expected value) of a discrete random variable.
Philip Stark, https://www.youtube.com/watch?v=hwF_jBdoQUA
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Khan Academy, https://www.youtube.com/watch?v=qafPcWNUiM8
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.