HELP! How do you find marginal frequency distributions in statistics? :)

Question

anonymous · Answer

You must be given a joint pdf of two jointly discrete/continuous random variables.

Whatever the case may be, if $f(x,y)$ is the joint pdf and $f(x)$ and $f(y)$ are the marginal pdf's of random variables $X$ and $Y$, respectively, then the marginal pdf of $X$ is
$$f(x)=\begin{cases}\displaystyle\sum_{y\text{'s}}f(x,y)&\text{if }X,Y\text{ discrete}\
\displaystyle\int_{-\infty}^\infty f(x,y)~dy&\text{if }X,Y\text{ continuous}\end{cases}$$
Alternatively, you can also get one random variable's marginal pdf if you're given the other's, as well as the conditional pdf, $f(x|y)$:
$$f(x)=\begin{cases}\displaystyle\sum_{y\text{'s}}f(x|y)f(y)&\text{if }X,Y\text{ discrete}\
\displaystyle\int_{-\infty}^\infty f(x|y)f(y)~dy&\text{if }X,Y\text{ continuous}\end{cases}$$

anonymous · Answer

It'd probably be easier to understand if you have an example...