Let $X_1,X_2,X_3$ be independent $Exp(\lambda)$ distributed random variables. I need to find $P(X_1<X_2<X_3)$.
I think we need to use independence, then we can rewrite $P(X_1<X_2<X_3)=P(X_1<X_2)P(X_2<X_3)$, 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.