Properties Of The Difference Of Random Variables

Let $X$ and $Y$ be independent random variables with respective means $\mu_X$ and $\mu_Y$. Let the random variable $Z = X - Y$. Consider the following statements.

I. The expected value of $Z$ is $\mu_X - \mu_Y$.
II. If $X$ and $Y$ have variances $\sigma_X^2$ and $\sigma_Y^2$, respectively, the variance of $Z$ is $\operatorname{Var}(Z) = \sigma_X^2 + \sigma_Y^2$.
III. If $X$ and $Y$ have standard deviations $\sigma_X$ and $\sigma_Y$, respectively, the standard deviation of $Z$ is $\sigma_X - \sigma_Y$.

Which of the above statements is or are true?