Suppose that $X \sim N(1, 2)$ and $Y \sim N(1, 2)$. Find 2 possibilities for the distribution of the difference $Z=X-Y$. State the conditions for each to apply.
The only possibility I could think of was $Z\sim N(0, 4)$. Can anyone suggest another possibility? The next part asks for the standardized form of $Z$ when $X$ and $Y$ are independent. I'm not too sure what the answer would be for this either.