Let $\mathbf{X}$ be an $n-$ dimensional random variable. This variable can be written as $\mathbf{X} = \left[\mathbf{X}_1^T\hspace{5pt}\mathbf{X}_2^T\right]^T$. where, $\mathbf{X}_1$ is $m-$ dimensional and $\mathbf{X}_2$ is $n-m$ dimensional. We can find the probability density function (pdf) of $\mathbf{X}$ as,
$p\left(\mathbf{X}\right) = p\left(\mathbf{X}_1,\hspace{3pt}\mathbf{X}_2\right)$ $=p\left(\mathbf{X}_1|\mathbf{X}_2\right)p\left(\mathbf{X}_2\right)$.
However, for the problem I am trying to solve, it's not possible (let's assume it) to find $p\left(\mathbf{X}_1|\mathbf{X}_2\right)$. But I can find $p\left(\mathbf{X}_1|\mathbf{X}_2=x_2\right)$. I also know $p\left(\mathbf{X}_2\right)$. How do I find $p\left(\mathbf{X}\right)$ from $p\left(\mathbf{X}_1|\mathbf{X}_2=x_2\right)$ and $p\left(\mathbf{X}_2\right)$?