For the two-sample energy statistic, prove that under the null hypothesis (H_{0}: X stackrel{D}{=} Y), the expected

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For the two-sample energy statistic, prove that under the null hypothesis \(H_{0}: X \stackrel{D}{=} Y\), the expected value of the test statistic \(\frac{n m}{n+m} \mathcal{E}_{n, m}(\mathbf{X}, \mathbf{Y})\) is \(E|X-Y|\).

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