How can I solve this problem? Is there any formula for this problem
Find the distribution of the random variable $Y$ if
- $Y=\min(X_1,X_2)$
- $Y=X_1+X_2$
where $X_1$ and $X_2$ are independent exponential random variables with means $\frac 1{\lambda_1}$ and $\frac 1{\lambda_2}$, respectively.