Does the law of total probabilites hold also in the case of continuous pdf?
$ f_{y} (y) = \int_{R}^{} f_{y|x}(s|t)f_{x}(t)dt $
2026-05-04 22:46:11.1777934771
Law of Total Probabilities for continuous pdf $ f_{y} (y) = \int_{R}^{} f_{y|x}(s|t)f_{x}(t)dt $?
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Close; $~~y$ needs to be the free variable on both sides of the equality.
$$f_Y(y) = \int_\Bbb R f_{X}(t)\,f_{Y\mid X}(y\mid t)\,\mathrm d t$$