This isn’t exactly on topic: I have only ever pronounced it ex-pair-eh-ment, but nearly all the cast of Big Bang Theory say ex-peer-eh-ment, which always kind of bugged me, until this thread reminded me to look into the matter.
It turns out my pronunciation is standard in US and UK English and the other way is a variation accepted by Merriam-Webster. The reason for that may have to do with the pronunciation of experience (or not?)