How do you sum PDF's of random variables? I have a question asking me to determine the PDF of $L=X+Y+W$, where $X$, $Y$ and $W$ are all independent. $X$ is a Bernoulli random variable with parameter $p$, $Y \sim \mathrm{Binomial}(10, 0.6)$ and $W$ is a Gaussian random variable with zero mean and unit variance (meaning is is a standard normal random variable).
I know the PDF's of $X$, $Y$ and $W$ (sort of hard to type out, but I know them). Could I get some sort of hint as to how these are added together?

The PDF of the sum of two independent variables is the convolution of the PDFs:
$$
f_{U+V}(x) = \left( f_{U} * f_{V} \right) (x)
$$
You can do this twice to get the PDF of three variables.
By the way, the Convolution theorem might be useful.
