Let [math]X[/math] be a continuous random variable with mean [math]\mu(X)[/math] and variance [math]\sigma^2(X)[/math], and let [math]X^* = (X - \mu)/\sigma[/math] be its standardized version. Verify directly that [math]\mu(X^*) = 0[/math] and [math]\sigma^2(X^*) = 1[/math].