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TL;DR

A random variable \( I_A \) that equals 1 if event A occurs and 0 otherwise. Its expectation is \( E[I_A] = P(A) \), and \( I_A^2 = I_A \).

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

Indicator Random Variable

A random variable \( I_A \) that equals 1 if event A occurs and 0 otherwise. Its expectation is \( E[I_A] = P(A) \), and \( I_A^2 = I_A \).

Why it matters for interviews

Indicator variables, combined with linearity of expectation, are the primary technique for computing expected counts in combinatorial probability. This method is ubiquitous in quant interviews.

Definition and Mathematical Foundation

A random variable \( I_A \) that equals 1 if event A occurs and 0 otherwise. Its expectation is \( E[I_A] = P(A) \), and \( I_A^2 = I_A \).

Application in Quantitative Finance

Indicator variables, combined with linearity of expectation, are the primary technique for computing expected counts in combinatorial probability. This method is ubiquitous in quant interviews.

Related Terms

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Frequently Asked Questions

How do you use indicators to find the expected number of records?▼
In a random permutation, the i-th element is a record (larger than all previous) with probability 1/i. Expected records: \( \sum_{i=1}^n 1/i = H_n \approx \ln n \). No independence needed.
Can indicators compute variance of counts?▼
Yes: \( \text{Var}(\sum I_i) = \sum \text{Var}(I_i) + 2\sum_{i<j} \text{Cov}(I_i, I_j) \). Each \( \text{Var}(I_i) = p_i(1-p_i) \), and the covariance terms require joint probability calculations.
What is the inclusion-exclusion connection?▼
\( P(\cup A_i) = E[1 - \prod(1-I_{A_i})] \). Expanding the product recovers inclusion-exclusion. Indicators provide a clean algebraic framework for combinatorial probability.