Let [math]X[/math], [math]Y[/math], and [math]Z[/math] be independent random variables, each with mean [math]\mu[/math] and variance [math]\sigma^2[/math].

• Find the expected value and variance of [math]S = X + Y + Z[/math].
• Find the expected value and variance of [math]A = (1/3)(X + Y + Z)[/math].
• Find the expected value of [math]S^2[/math] and [math]A^2[/math].