Conceptual analogy between mass density and probability density – An almost non-technical note

Author:

Bokor László

Abstract

<abstract> <p>I show how multivariate integration over a physical object serves as a handy tool for a gentle introduction to multivariate probability theory with continuous variables. This exercise helps to visualise and thus link concepts that at first sight seem distant or even unrelated. The concepts and methods presented are digestible for advanced high school classes and above.</p> </abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference5 articles.

1. Presnell, B., A Geometric Derivation of the Cantor Distribution. The American Statistician, 2022, 76(1): 73‒77. https://doi.org/10.1080/00031305.2021.1905062

2. Smith, D.J., Vamanamurthy, M.K., How Small Is a Unit Ball? Mathematics Magazine, 1989, 62(2): 101‒107. https://doi.org/10.1080/0025570X.1989.11977419

3. Solomon, H., Geometric Probability – CBMS-NSF Regional Conference Series in Applied Mathematics No. 28, 1978, Society for Industrial and Applied Mathematics.

4. Klain, D.A., Rota, G-C., Introduction to Geometric Probability, 1997, Cambridge University Press.

5. Mathai, A.M., An Introduction to Geometrical Probability: Distributional Aspects with Applications, 1999, CRC Press.

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