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→实例4 - 辛普森悖论
<math>
<math>
P(Y=1|do(X=0)) = \sum_Z P(Y=1|X=0, Z=z)P(Z) <br>
\begin{align}
= P(Y=1|X=0, Z=1)P(Z=1) + P(Y=1|X=0, Z=0)P(Z=0) <br>
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
= \frac{0.87*(87+270)}{700} + \frac{0.69*(263+80)}{700} = 0.781
\end{align}
</math>
</math>