= Solution
{c}
The marginal <probability density function> is $f_Y(y)=\int_{\mathbb R}f_{X,Y}(x,y)\,dx$. For $y$ with $f_Y(y)>0$, the <conditional density> is
$$
\boxed{f_{X\mid Y=y}(x)=\frac{f_{X,Y}(x,y)}{f_Y(y)}.}
$$
If the conditional first absolute moment is finite, the <conditional expectation> is
$$
\boxed{\mathbb E[X\mid Y=y]=\int_{\mathbb R}x\,\frac{f_{X,Y}(x,y)}{f_Y(y)}\,dx.}
$$
Conditioning here uses a density, since the individual event $Y=y$ normally has probability zero; a conditional law is specified only up to marginal-null values of $y$.
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