I have a problem with this exercise:
I have to calculate the convolution of two independent Bernoulli distributions, each with parameter $p$ random variables.
Let $X$ and $Y$ be te two random variables:
The definition of convolution is: $f_{x+y=z}=\sum_{i=0}^k f_x(i)f_y(k-i)$
Proceeding with the definition I have $f_{x+y=z}=\sum_{i=0}^1 f_x(i)f_y(1-i)=\\f_x(0)f_y(1)+f_x(1)f_y(0)=2(f_x(0)f_x(1))$
The last equation is because they have the same $p$.
So I have:
$f_{x+y=z}=2(p^0(1-p)^1p(1-p)^0)=2p(1-p)$
Did I make some mistakes or is everything right?