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

László Bokor; László Bokor

doi:10.3934/steme.2024009

STEM Education

2024, Volume 4, Issue 2: 142-150. doi: 10.3934/steme.2024009

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Technical note

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

László Bokor ^,

Budapest, Hungary

Academic Editor: Chris Tisdell

Received: 03 December 2023 Revised: 05 March 2024 Accepted: 06 March 2024 Published: 19 March 2024

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.
- multivariate probability,
- continuous random variable,
- density,
- physical space,
- analogy,
- dimensionality,
- shape
Citation: László Bokor. Conceptual analogy between mass density and probability density – An almost non-technical note[J]. STEM Education, 2024, 4(2): 142-150. doi: 10.3934/steme.2024009

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Abstract

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.

References

[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 doi: 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 doi: 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.

Author's biography Dr. László Bokor is an economist. His research interests are monetary policy, antitrust economics, and green finance

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