To a 'rational' mind, none of Arthur's jokes are funny.
To my recollection, he doesn't make one 'actually funny' statement in the entire movie. He doesn't laugh at things that other people say that are, & he responds 'incorrectly' to some that aren't.
[This is aside from his well-acknowledged 'nervous laugh' when under emotional pressure, and not to be confused with that.]
From a cinematic perspective, someone had to actually construct that page for the audience to see it wasn't a single thought on an otherwise blank page, but also to be credible if, as we're doing here, someone snapshots the page to read and examine at leisure later.
Arthur has grasped the idea that a simple two-liner joke sets up a premise, then destroys it by having the punch-line either reverse that premise by 'surprise', or at least leave a double-entendre as to which of two interpretations could be the correct one.
The jokes you see on that page are written evidence of that, all neatly in one place for us to grab a snapshot and examine after the fact.
Insomniac doesn't want to sleep with his wife - play on words… 'sleep' - not funny.
Poor people are confused because they don't make any cents.
another play on words… not funny.
He used this sense/cents elsewhere in the movie, establishing his failure to grasp that just because it's a play on words doesn't actually in and of itself make it funny.
You say to a straight-jacket, "Loosen up a little." - which is the closest you get to a 'real joke' except that the subject matter is 'mental patient' & most comedy club audiences don't comprise that demographic, even if they probably understand it as 'a joke'… so it's a stretch.
Personally, I think that one is to give the cinema audience a clearer guide as to his thought processes. Had he told that joke as part of a recognised 'actually funny' act, it may have got a laugh. Just because a stand-up comic gets close to the edge doesn't make them not funny, even if their audience can only imagine the real-life circumstance. Arthur doesn't grasp this & I feel cinematically we're expected to see this as a character flaw rather than edgy comedy.
So the last one - the joke we actually get time enough to read as the action unfolds is an extrapolation of that. The audience is given the chance to see what he is writing whilst ostensibly taking notes on how a comedian structures his act live on stage. Arthur so clearly doesn't "get it". He's seen to be laughing in all the wrong places.
This is a 'movie short-cut' allowing the audience to see what he is thinking whilst supposedly taking notes on what he is seeing.