About this question
Medium · Probability & Statistics · Quant Trader interview question · probability, expected-value, conditional-expectation, tower-property
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 $EEX | Y = EX$.