My fav way to intuit this is this example https://stats.stackexchange.com/questions/85363/simple-examples-of-uncorrelated-but-not-independent-x-and-y https://s

My fav way to intuit this is this example https://stats.stackexchange.com/questions/85363/simple-examples-of-uncorrelated-but-not-independent-x-and-y https://stats.stackexchange.com/questions/85363/simple-examp... Blew my mind the first time I saw it. Not the same definitions one to one (author specifically talks about correlation vs linear correlation) but same idea.