I need some insights on solving the probability and statistics problems. Specifically, I was studying a review notes and among my searches I encountered this link.
I understood the proof by plotting the equation for $x_2-x_1 \leq y$ using different values of y and it took me a long time. I passed calculus and statistics long time ago and I am not skilled in solving these problems. My question is plotting the equation is the only way to writing the integration boundaries? Is there any methods that can be done faster with less error rather than plotting?
I appreciate any insights you can provide.
Thanks.