# Math Help - independent exponential random variables having a common parameter

1. ## 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!!

2. Hello,

Work with the cdfs... :

Let x>0
$P(\min(X_1,\dots,X_n)\leq x)=1-P(\min(X_1,\dots,X_n)>x)$

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

So $P(\min(X_1,\dots,X_n)\leq x)=1-P(X_1>x,\dots,X_n>x)$

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