As a former engineering student, I have a great interest in a real world application of mathematics. Probability is something I can relate to. I am lucky enough that after I switched to Mathematics, this is one of many interests of my Ph.D. advisor, Doron Zeilberger, as well. In this article we create a program to apply the \textit{overlapping stage approach} to calculate the moments $E[X^r]$ and $E[(X-μ)^r]$ of combinatorial objects. We also show the normality property of their distributions when these moments are easy enough to calculate.
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