Show that the PSD function of a WSS random process \(\{X\}\) satisfies the following properties:

(a) \(\Gamma_{X}(0)=\sum_{v=-\infty}^{\infty} R_{X}(v)\).

(b) It is an even function; that is: \(\Gamma_{X}\left(\mathrm{e}^{\mathrm{j} \omega}\right)=\Gamma_{X}\left(\mathrm{e}^{-\mathrm{j} \omega}\right)\), for all \(\omega\).

(c) It is a nonnegative function; that is: \(\Gamma_{X}\left(\mathrm{e}^{\mathrm{j} \omega}\right) \geq 0\), for all \(\omega\).