Conditional Expectation Tower Property - Quant Trader Interview Question
Difficulty: Medium
Category: Probability & Statistics
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: probability, expected-value, conditional-expectation, tower-property
Problem Description
Let $X$ be a random variable representing the profit (in dollars) from a trading strategy, and let $Y$ be another random variable representing a market indicator (e.g., VIX level). You are trying to understand how the expected profit of your strategy relates to the market indicator. The conditional expectation of $X$ given $Y$, denoted $EX | Y$, represents the expected profit given a specific value of the market indicator. The tower property of conditional expectation states that $EEX | Y = EX$.
Practice this medium trader interview question on MyntBit - the all-in-one quant learning platform with 200+ quant interview questions for Jane Street, Citadel, Two Sigma, and other top quantitative finance firms.