Thread: independent exponential random variables having a common parameter

Let X1, X2, ...Xn be independent exponential random variables having a common parameter gamma. Determine the distribution of min(X1, X2, ...Xn)
Thank you!!

Hello,

Work with the cdfs... :

Let x>0


But if the min is > x, this means that all the Xi's are > x.

So

now use the independence to write it as a product of probabilities and finish it off