Can any of you help me? I have some problem with this exercise of "Probability and Statistics" :
Calculate the probability density function (PDF) of $Z=X+Y$
where $Y$ is discrete random variable which is be equal to $-1,1$ with equal probability; $X$ is standard Gaussian random variable independent from $Y$.
I know that the PDF of sum of two continuous independent variables is given by the convolution of the marginal PDF $f_z(z)=f_x*f_y$ but if one on the two variable is discrete what should I do? thanks all!