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TL;DR

The probability distribution of a subset of random variables obtained by integrating (or summing) out the other variables from a joint distribution.

By Valenke Exam Prep Team·Last updated 2026-06-03

Marginal Distribution

The probability distribution of a subset of random variables obtained by integrating (or summing) out the other variables from a joint distribution.

Why it matters for interviews

Quant interviews frequently require extracting marginal distributions from joint setups. Understanding marginalization is essential for Bayesian updating and multivariate probability problems.

Definition and Mathematical Foundation

The probability distribution of a subset of random variables obtained by integrating (or summing) out the other variables from a joint distribution.

Application in Quantitative Finance

Quant interviews frequently require extracting marginal distributions from joint setups. Understanding marginalization is essential for Bayesian updating and multivariate probability problems.

Related Terms

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Frequently Asked Questions

Can you recover a joint distribution from marginals alone?▼
No. Marginals do not capture the dependence structure. Different joint distributions can share the same marginals but differ in their copula (dependence). Additional information about correlation or copula is needed.
How are marginal distributions used in risk management?▼
Individual asset return distributions (marginals) are combined with a copula or correlation matrix to model portfolio-level risk. VaR at the portfolio level requires understanding joint behavior, not just marginals.
What is the relationship between marginal and conditional distributions?▼
The conditional distribution \( f(y|x) = f(x,y)/f_X(x) \) uses both the joint and marginal. The marginal can be recovered from conditionals via \( f_X(x) = \int f(x,y)dy \).