Conditional Independence and Marginal Independence - Quant Trader Interview Question
Difficulty: Medium
Category: Conditional Probability
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Topics: probability, conditional-probability, independence, trading-strategy
Problem Description
Suppose you are analyzing the performance of two algorithmic trading strategies, A and B, on days when the VIX index is above 20. Let C be the event that the VIX index is above 20 on a given day. You observe that strategies A and B's returns are conditionally independent given C.
Specifically, let A be the event that strategy A is profitable on a given day, and let B be the event that strategy B is profitable on the same day. You are told that $P(A \cap B | C) = P(A | C) P(B | C)$.
Does this c
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