if we have a PDF of a random variable X with a parameter, let's say $f_X(x;b)=2xb$ is it possible to find an expression for the unconditional pdf of X if the parameter b follows another known distribution?
Thanks:)
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$\begingroup$ Presumably there is more detail, such as that $0\le X \le \frac1{\sqrt{b}}$ and $b>0$. But in theory yes, and in practice yes for some distributions of $b$ $\endgroup$– HenryCommented Mar 6, 2022 at 1:40
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The pdf of $X$ can be computed as such:
$$f_X(x; B) = \int_b f_X(x; b) f_B(b) \, db$$
Here are some readings on marginal distribution.
answered Mar 6, 2022 at 4:14