Abstract
Probability and statistics are the central components of many ideas in science and industry. The goal of this chapter is not to give a general introduction to probability, but to give a taste for how generating functions can unlock probabilistic results for combinatorial problems. In this chapter we will explore how the mean and variance of probability distributions can be extracted from generating functions, with sometimes surprising results about the behavior of “random" combinatorial models.
“Creativity is the ability to introduce order into the randomness of nature."
–Eric Hoffer
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Petersen, T.K. (2019). Applications to probability. In: Inquiry-Based Enumerative Combinatorics. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-18308-0_11
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DOI: https://doi.org/10.1007/978-3-030-18308-0_11
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-18308-0
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