I am currently trying to figure out a problem and it is using notation that I have never seen before so I am pretty stuck, any suggestions would be greatly appreciated!
Let $X, Y, Z$ be independent exponential random variables with the same mean, $σ$. Find the value of $σ$ so that $\Pr[\max(X,Y,Z)>1]=0.05$.
Any help with how to solve this problem or leading down the right path would be awesome as I am not to sure where to even start!
EDIT: So I have followed what André Nicolas has said and got a $σ$ of $0.25$. However I am still not sure where he got this formula from: The probability they are all $\le a$ is $(1-e^{-a/\sigma})^3$.
I cant find anything like this is my notes or textbook, could any reference where he got this?
Answer
A start: The probability that $\max(X,Y,Z)\gt 1$ is $1$ minus the probability they are all $\le 1$.
The probability they are all $\le a$ is $(1-e^{-a/\sigma})^3$.
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