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PreprintCC BY 4.0arXiv

The importance of the change-of-variables integration technique in deriving the PDFs of important probability distributions

  • Jorge P. Arpasi
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Abstract

The purpose of this article is to explicitly describe how the integration technique known as the change of variables is used in graduate-level Probability and Statistics courses. Throughout the article, we employ this integration technique seven times across various examples and results. We demonstrate that four applications of this technique are required to derive the probability density function (PDF) of the Student's t-distribution.

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Cite

BibTeXRIS
BibTeX
@misc{arpasi2026importance,
  title = {{The importance of the change-of-variables integration technique in deriving the PDFs of important probability distributions}},
  author = {Jorge P. Arpasi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30529},
  eprint = {2609.30529},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30529},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The importance of the change-of-variables integration technique in deriving the PDFs of important probability distributions
AU  - Jorge P. Arpasi
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30529
UR  - https://arxiv.org/abs/2609.30529
AB  - The purpose of this article is to explicitly describe how the integration technique known as the change of variables is used in graduate-level Probability and Statistics courses. Throughout the article, we employ this integration technique seven times across various examples and results. We demonstrate that four applications of this technique are required to derive the probability density function (PDF) of the Student's t-distribution.
ER  -