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Two Sigma Quant Interview Questions

Two Sigma is one of the world’s most prestigious quantitative hedge funds, known for its rigorous hiring process and challenging interview questions. Quantitative research interview questions at Two Sigma are designed to test your understanding of probability, statistics, and problem-solving abilities.

Let \( X \) and \( Y \) be random variables with standard deviations \( a \) and \( b \) respectively. What are the bounds of \( \mathrm{Var}(X + Y) \)?

We are given: