If X has mean µ and standard deviation σ , the ratio  is called the measurement signal-to-...

If X has mean µ and standard deviation σ , the ratio  is called the measurement signal-to-noise ratio of X. The idea is that X can be expressed as X = µ + (X − µ), with µ representing the signal and X − µ the noise. If we define  as the relative deviation of X from its signal (or mean) µ, show that for α > 0,