Distribution of Product of Random Variables with one being the normal distribution.
\begin{align} P(Y\le y)&=P(XZ\le y)\\ &=0.5P(X\le y)+0.5P(-X\le y)\\ &=P(X\le y)\text{ (using distribution's symmetry)} \end{align}
Distribution of Product of Random Variables with one being the normal distribution.
\begin{align} P(Y\le y)&=P(XZ\le y)\\ &=0.5P(X\le y)+0.5P(-X\le y)\\ &=P(X\le y)\text{ (using distribution's symmetry)} \end{align}