Let [math]X[/math] be a random variable with range [math][-1,1][/math] and [math]f_X[/math] its density function. Find [math]\mu(X)[/math] and [math]\sigma^2(X)[/math] if, for [math]|x| \gt 1[/math], [math]f_X(x) = 0[/math], and for [math]|x| \lt 1[/math],

• [math]f_X(x) = (3/4)(1 - x^2)[/math].
• [math]f_X(x) = (\pi/4)\cos(\pi x/2)[/math].
• [math]f_X(x) = (x + 1)/2[/math].
• [math]f_X(x) = (3/8)(x + 1)^2[/math].