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How can I solve this problem? Is there any formula for this problem

Find the distribution of the random variable $Y$ if

  1. $Y=\min(X_1,X_2)$
  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.

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