Find the probability mass function of the sum of X ∼ Bernoulli(p) and an independent Y ∼ Bernoulli(q) variable.
I started by letting Z=X+Y
So $$P_z(Z)= \sum_{i=0}^{1}f_x(x) f_y(z-x) $$
$$ \sum_{i=0}^{1}\dbinom{1}{x} p^{x}(1-p)^{1-x} \dbinom{1}{z-x} q^{z-x}(1-q)^{1-z+x} $$ I am unsure as to how I can evaluate this
Thankyou for your help