Let $X$ and $Z$ be continuous random variables. Let a conditional PDF be defined as $f\left(X\big|Z\right)$. To use total probability theorem (TBT), we introduce a discrete random variable $\Theta$ as given $$f\left(X\big|Z\right) = \sum_{\theta}f\left(X,\Theta = \theta\big|Z\right)$$ The question is, how to use TBT of we have two or more discrete random variables $\Theta_1$, $\Theta_2$, $\ldots$, $\Theta_N$?

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    $\begingroup$ $$f\left(X\big|Z\right) = \sum_{\theta_1} \sum_{\theta_2} \ldots \sum_{\theta_N} f\left( X, \Theta_1 = \theta_1, \Theta_2 = \theta_2, \ldots , \Theta_N = \theta_N \big| Z \right)$$ $\endgroup$ – Ertxiem May 22 at 11:54

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