How to derive correlation from variances
Company: Jefferies
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
You have two random variables X and Y.
You are given:
- Var(X + Y)
- Var(X)
1) Is the correlation Corr(X, Y) identifiable from only these two quantities? Explain why/why not.
2) If, in addition, you are also given Var(Y), derive Corr(X, Y) in terms of Var(X + Y), Var(X), and Var(Y).
Assume finite second moments and that all variances are computed under the same probability model.
Quick Answer: Tests understanding of variance–covariance relationships and identifiability of correlation from aggregate variance statistics, within the Statistics & Math domain for a Data Scientist role.