Let [math]X[/math] be a random variable with range [math][-1,1][/math] and let [math]f_X(x)[/math] be the density function of [math]X[/math]. Find [math]\mu(X)[/math] and [math]\sigma^2(X)[/math] if, for [math]|x| \lt 1[/math],

• [math]f_X(x) = 1/2[/math].
• [math]f_X(x) = |x|[/math].
• [math]f_X(x) = 1 - |x|[/math].
• [math]f_X(x) = (3/2) x^2[/math].