Are there any real studies that have been done to see what the
personality types of children are given two parents with certain
personality types?

I'm thinking specifically of broad categories like Meyers-Briggs
types. I know those types aren't biological, they're just measurements
of the personality that a person has for whatever reason that they
have it.

For example, on a percentage basis, if two INTJ parents have children,
what is the % likelihood that the child will turn out to be INTJ when
they reach the same age as their parents were at the time of the
child's birth?

If one parent is INTJ and the other is ESFP then what is the %
likelihood that the child will end up with any given personality type?

If the dad is INTJ and the mother is ESFP then would a male child more
likely to be INTJ than ESFP compared to the community average? Would a
female child be more likely to be ESFP than INTJ compared to the
community average?

I'm curious because this sort of analysis would circumvent any sort of
nature vs. nurture issues. In a given community a parent with a
particular personality type would raise their kids in a certain way as
well as have biology that contributed to making them that way.

I'm curious about how much the personality type of the dad contributes
to the personality type of a daughter (and the same for a mom and a
son) compared to the contribution made by the parent of the same
gender.

Obviously there are other issues like the personality differences that
result from being the first born versus second born, etc., but that
could be controlled by just comparing first born to first born and
second born to second born in families of identical sizes.

It would also be interesting to know if certain personality types were
more likely to be passed than others.