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408.Sum Versus Gap

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geometric probabilityCh. 4 — Continuous Distributions and Moments444+ Problems in Probability
Let X,Y∼Unif(0,1)X, Y \sim \mathrm{Unif}(0,1) IID. Compute P[X+Y≥2 ∣X−Y∣]P[X + Y \ge 2\,|X - Y|].

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