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→实例4 - 辛普森悖论
<math>
<math>
P(Y=y|do(X=1)) = \sum_Z P(Y=y|X=x, Z=z)
P(Y=1|do(X=1)) & = \sum_Z P(Y=1|X=1, Z=z)P(Z) = P(Y=1|X=1, Z=1)P(Z=1) + P(Y=1|X=1, Z=0)P(Z=0)
& = \frac{0.93*(87+270)}{700} + \frac{0.73*(263+80)}{700} = 0.832
</math>
同理，
<math>
P(Y=1|do(X=0)) & = \sum_Z P(Y=1|X=0, Z=z)P(Z) = P(Y=1|X=0, Z=1)P(Z=1) + P(Y=1|X=0, Z=0)P(Z=0)
& = \frac{0.87*(87+270)}{700} + \frac{0.69*(263+80)}{700} = 0.781
</math>
因此，服用药物的效果和不服用药物的效果的差异为：
<math>
P(Y=y|do(X=1)) - P(Y=y|do(X=0)) = 0.832 - 0.781 = 0.0502
</math>
</math>