Marginals of the PDF $f(x,y) = \frac{3}{2}(x^2 y + y)$ for $x,y \in [0,1]$

Question

For a given pdf

$$f(x,y) = \frac{3}{2}(x^2 y + y)$$

where $x,y \in [0,1]$.

Am I right in saying the marginal pdf of X is $\frac{3}{4}(x^2 + 1)$, and the marginal pdf of Y is $2y$.

Cheers

Answer 1

Yes, the answer is correct.

$$f(x,y) = \frac32(x^2+1)y$$

To find marginal distribution of $X$, integrate with respect to $y$ from $0$ to $1$.

Similar for $Y$.