Is it possible to reasonably guess the gender of a person from a random sample of their writing (text, not handwriting)?
How about from the contents of their speech (not including their voice, of course)?
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While you are probably better to ask your question over at the AI Stack Exchange for more practical answers on how to accomplish the task, I would also suggest you could take a look into the topics on Wikipedia for Sociolinguistics, and also Language and gender for the underlying theories as to why Machine learning models are able to make guesses/predictions with upwards of 80% accuracy in trained models such as the following.
So to fully answer your question
Can one reasonably guess the gender of a person from their writing/speech contents?
What is a 'reasonable guess' is not something I can define and is something you would wan't to think seriously about before using the predictions for anything of import to those you are labelling! However it would seem you can make a significantly better than random guess.
Guesswork is not what this site is about.
Statistical analysis of factors of "The Big 5" personality traits:
have been extensivley studied and are well understood in terms of the sex differences that emerge from biology, and also but less so from cultural differences.
It would be possible to design studies to research the various different modes and media of writing, given sufficient funding and analytical clout to do what you ask.
As far as this answerer can determine, no-one has yet given it much attention as it is a low-priority compared to the social issues that prevail in societies today. What you are asking would be considered trivial or "Blue Sky" research at best.
Statistical analysis of many factors, correcting for others is (reductio) extended inductive reasoning, which is (reductio ad absurdum) guesswork.
Get the financial backing to gather a big enough (set of) sample(s) that you can leverage analysis out of (and the mental tools to bring it to order) and you're all set to make a "guess".