Assume we have random variable $W =\max(X,Y) - X$, I would like to find the pdf of $W$. Here, X, Y are independent continuous random variables. Does the following work? $$ F_W(w)=\mathbb{P}[W≤w]=\mathbb{P}[\max(X,Y)-X≤w]=\mathbb{P}[0≤w]\mathbb{P}[Y-X≤w]=F_X(w)F_Y(w+x) $$ And then what should I do?
2026-03-26 17:30:49.1774546249
Probability density function of max(X,Y) - X
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