"Let $U, V,$ and $W$ be independent random variables with equal variances $\sigma^2$. Define $X=U+W$ and $Y=V-W$. Find the covariance between $X$ and $Y$."
Since $U,V$, and $W$ are independent, I know that I can calculate the variance of $X$ and $Y$ as $\sigma^2 + \sigma^2$. However, I don't see how to use this information to calculate the covariance between $X$ and $Y$. In the formula given for covariance, it seems like I would need to know the mean of $X$ and $Y$ to do this calculation.
If you know some properties of the covariance, we can do the following:
$$\begin{align*}\text{cov}(X,Y) &= \text{cov}(U+W,V-W) \\ &= \text{cov}(U,V) + \text{cov}(W,V) - \text{cov}(U,W) - \text{cov}(W,W) \\ &= 0 + 0 - 0 - \text{var}(W) \\ &= -\sigma^2\end{align*}$$