Sum of Random Variables

The Problem

Let $X$ and $Y$ be independent random variables with $X\sim \mathcal{N}({\mu }_X,{\sigma }_X^2)$ and $Y\sim \mathcal{N}({\mu }_Y,{\sigma }_Y^2)$.

1. What is the distribution of $X+Y$?
2. What is the distribution of $\max (X,Y)$?
3. Convolution: Let $X\sim \text{Exponential}(\lambda )$ and $Y\sim \text{Exponential}(\mu )$ be independent. What is the density of $X+Y$? (Hint: not exponential unless $\lambda =\mu$.)