Answer

PDF $f_X(x)$: $P(x<X\le x+dx)=f_X(x)dx$, $\int f=1$, $F_X(x)=\int_{-\infty}^x f$. CDF $F_X(x)=P(X\le x)$: monotonic 0→1, $f=dF/dx$. Gaussian $f=(1/\sqrt{2\pi}\sigma)e^{-(x-\mu)^2/2\sigma^2}$, $F=\Phi((x-\mu)/\sigma)$. Use for BER via $Q$.