From the famous alleywaystotorah blog:-)
Avromi was a young man who was pious and devout. What they call today Charedi or
Ultra Orthodox [how come irreligious people are not called "Ultra Secular"?].
One Chol Hamoed Succos Avromi found out that his mother [the daughter of
holocaust survivors] was not Jewish! Making Avromi a ..... Goy. With a capital
G.
Uh oh.
So of course Avromi wanted to convert, but the question
was, is there any reason for him to sit in a succah in the meantime.
Answer: YES! The Rambam [Melachim 10/10] says that a gentile who wants
to keep a given commandment [besides shabbos] in order to receive reward should
not be prevented from doing so. We learn from this Rambam that a goy may fulfill
mitzvos and will be rewarded for his efforts.
So sit in the succah
Avromi, sit. And if you wish you may also have a juicy cheeseburger. Wow! A
mitzva to sit in the succah while eating a cheeseburger ["simchas yom tov"].
Isn't Torah interesting?!
See Kovetz Shiurim Simman 54 and Chashukei
Chemed page 212 for a discussion of how the Rambam's law squares with the
talmudic principle that anyone who is exempt and nevertheless fulfills the
mitzva is acting silly [kol hapatur min hamitzva viosehu nikra hedyot].