# difference of two independent exponentially distributed random variables

Let $$X_1,X_2,X_3$$ be independent $$Exp(\lambda)$$ distributed random variables. I need to find $$P(X_1.

I think we need to use independence, then we can rewrite $$P(X_1, but I don't know how to proceed next. Maybe considering $$Y=X_1-X_2$$, but then we need to find the distribution of Y, which is hard for me.

Any help would be appreciated, thanks.

\begin{align}P(X_1
Since they have to sum up to $$1$$, $$P(X_1