Select random value for each row

I'm trying to select a new random value from a column in another table for each row of a table I'm updating. I'm getting the random value, however I can't get it to change for each row. Any ideas? Here's the code:

UPDATE srs1.courseedition
SET ta_id = teacherassistant.ta_id
FROM srs1.teacherassistant
WHERE (SELECT ta_id FROM srs1.teacherassistant ORDER BY RANDOM()
       LIMIT 1) = teacherassistant.ta_id