Okay, so I have this problem that states $X$~$Exponential(2)$, and $Z$~$Exponential(2)$ where Z is independent from $X$. The problem that I'm trying to solve wants me to find the distribution $X+Z$ and find the $Var(X-Z)$.
The first part of the question is to find the distribution of $X+Z$. I'm not sure if I need to calculate something from this or just realize that when we are adding to Exponential distribution, we can use the Gamma distribution. So to the first question my answer would be: $X+Z$~$\Gamma(2,2)$.
The second question is to find the variance of $X-Z$. Here my first thought is to use the definiton of variance for Gamma distributions, which is $Var(X)=\alpha/\lambda^2$. In this case my answer would be $Var(X-Z)=2/2^2$$=1/2$.
I would, of course, like to know if I'm right or wrong. And if I'm wrong what would you recommend that I do instead? Btw I'm pretty new to statistics and trying to learn.