explain this formula and give me an example

Risk-adjusted returns \\[ S I_{p}=\\frac{R_{p}-R_{f}}{\\sigma_{p}} \\] Vhere \\( S I_{p}= \\) Sharpe index/ratio \\( R_{p}= \\) return on fund or portfolio \\( R_{f}^{p}= \\) risk-free rate of return \\( \\sigma_{p}=\\mathrm{SD} \\) of fund returns \\( \\underline{\\text { (net of risk free) }} \\) Risk-adjusted returns \\[ \\begin{array}{c} T R=\\left(R_{p}-R_{f}\ ight) / \\beta_{p} \\\\ \\text { Alpha }=R_{p}-\\left[R_{f}+\\left(E\\left(R_{m}\ ight)-R_{f}\ ight) \\beta_{p}\ ight] \\end{array} \\] Where \\( R_{p}= \\) return on fund or portfolio \\( R_{f}= \\) risk-free rate of return \\( \\beta_{p}= \\) Systematic risk of fund/portfolio