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What is the purpose of those capicators between the line and the ground?

These caps help to filter out switching noise comming from the unit's power supply, and also gives a consistant path for RF of TV frequencies that happen to be picked up by the power wiring to get to the unit's tuner. Else "hum modulation" can happen trashing reception.

3 wire equipment like computers and computer monitors also have these caps. But the ground usually drains it off. Once at a company I was working for we were having random failures of electronic equipment under test. When connecting some video cables from across the room I got a mild shock with this setup. Investigated, and found a bad ground in an extension cord we were using.