Show that the autocorrelation function of a WSS process ({X}) presents the following properties: (a) (R_{X}(0)=Eleft{X^{2}(n) ight})

Show that the autocorrelation function of a WSS process \(\{X\}\) presents the following properties:

(a) \(R_{X}(0)=E\left\{X^{2}(n)\right\}\)

(b) it is an even function; that is: \(R_{X}(v)=R_{X}(-v)\), for all \(v\)

(c) it has a maximum at \(v=0\); that is: \(R_{X}(0) \geq\left|R_{X}(v)\right|\), for all \(v\).