On using "I" in expository essays - I dunno about personal anecdotes, but just saying "I" is pretty acceptable, I think. (I'm honestly no expert, everyone in this thread would know more about expos. than I would) - I remember a thread in 2012 - the user Charmanderp was talking about it and he said it really assisted his writing. He posted an essay up once, it was pretty phenomenal from memory.
Personally, I wouldn't hugely advocate the use of personal anecdotes, they could come off really shitty, shallow, irrelevant, and you probably think they're a lot more moving than they actually are because you can't be fully objective about your own writing while you're writing it (unless you become very skilled). However, there's exceptions to everything when a possibility to hit criteria comes in. If I somehow got a prompt on like.... Failing school and then doing awesome in school and how it feels, I'd be using a fuckload of anecdotes and I'd be so darn emotional they'd have to give me a 10. Use your discretion, referring to yourself in a personal way can often lead to shitty writing. (Almost every 1st person story a classmate every showed me in 2012 made me want to punch myself)