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Probability: Difference between revisions
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{{hidden | Proof | | {{hidden | Proof | | ||
<math> | <math> | ||
E(X) = \int_S x p(x)dx | \begin{aligned} | ||
= \int_x x \int_y p(x,y)dy dx | E(X) &= \int_S x p(x)dx \\ | ||
= \int_x x \int_y p(x|y)p(y)dy dx | &= \int_x x \int_y p(x,y)dy dx \\ | ||
= \int_y\int_x x p(x|y)dxp(y)dy | &= \int_x x \int_y p(x|y)p(y)dy dx \\ | ||
&= \int_y\int_x x p(x|y)dxp(y)dy | |||
\end{aligned} | |||
</math> | </math> | ||
}} | }} | ||