Multiple independent exponential random variables

[libragirl79]

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

The Attempt at a Solution

I know how to do it with one X and one parameter but I am at a loss with these multiple ones...

Thanks so much!

 

[grief]

Hint: min(X1,X2,...Xn)>x is equivalent to saying X1>x and X2>x and... Xn>x.

You can find the latter probability by multiplying the probabilities of each event.