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Probability and Statistics · Easy

Variance of Two Variables

Original interpretation · Match confidence: medium

Jane Street · Topic guidanceSusquehanna (SIG) · Topic guidanceCitadel · Topic guidance
About this question’s source match

The title and category identify the topic, but no accessible evidence establishes the hidden catalogue statement. This is an original numerical practice question on that specific topic. The hidden Trading Interview wording, parameters and requested subparts have not been verified.

X and Y have variances 4 and 9 and covariance 1. Find Var(X+Y), Var(X-Y), and Var(2X-3Y). Do you need independence?

Assumptions and constraints

  • Finite second moments.
  • All moments use consistent units and observation horizon.
  • Answer every requested subpart and justify your reasoning.

Examples

Var(X)=Var(Y)=1, Cov=1
→ Var(X-Y)=0

Perfect positive correlation can cancel difference risk.

Company preparation relevance

These links connect this exercise to companies’ public examples or stated interview topics. They do not establish that a company asked this exact Learnr question.

  • Jane Street

    Official topic guidance

    Topic overlap: expected-value decisions “Cash or Reroll”, additive waiting expectations “Collecting Stickers”, and dependence in “Variance of Two Variables” connect to the guide’s expectation, linearity and independence sections.

    Probability & Markets — official guide ↗
    Evidence scope and uncertainty

    General probability preparation; numerical tasks and structures beyond those topics are Learnr choices.

    These are Learnr-authored exercises selected for topic overlap. The company does not name these catalogue titles or verify that these exact questions were asked.

  • Susquehanna (SIG)

    Official topic guidance

    Topic overlap: variance “Variance of Two Variables” and linear-algebra exercises “Gram-Schmidt Process”/“Rank” align with a recruiter responsibility to create interview questions in probability, statistics, calculus and linear algebra.

    Quantitative Recruiter — official job posting11568 ↗
    Evidence scope and uncertainty

    Primary employer posting read through its search-indexed content; direct fetch returned an error. The posting concerns recruiting responsibilities, not a disclosed applicant question list.

    Topic categories are present in the indexed official posting. No statement confirms these exercises were used, and job postings can change or expire.

  • Citadel

    Official topic guidance

    Topic overlap: least-squares modeling “Deriving OLS”, Gaussian parameter estimation “Maximum Likelihood Estimation for a Gaussian” and dependence/variance “Variance of Two Variables” practice the mathematical/statistical intuition and data-modeling skills named in the FAQ.

    Candidate FAQs: Quantitative Research ↗
    Evidence scope and uncertainty

    Research skill preparation. The FAQ describes candidate strengths and work rather than publishing these particular interview exercises.

    These are Learnr-authored exercises selected for topic overlap. The company does not name these catalogue titles or verify that these exact questions were asked.

References

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Catalogue metadata captured 2026-10-12. Metadata source.