证明：右边=∫[0→+∞] [1-F(x)]dx - ∫[-∞→0] F(x)dx
下面用分部积分
=x[1-F(x)] |[0→+∞] + ∫[0→+∞] xF'(x)dx - xF(x)|[-∞→0] + ∫[-∞→0] xF'(x)dx
=0 + ∫[0→+∞] xf(x) dx - 0 + ∫[-∞→0] xf(x) dx
=∫[-∞→+∞] xf(x) dx
=E(x)=左边
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