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Quote from kiligir1. You can choose to cast any of the instants or sorceries, and yes they will go to your graveyard upon resolution.
Quote from SamuraiMunkyFrom the rulings found in the description of the card on magiccards.info
"If you cast a card “without paying its mana cost,” you can’t pay alternative costs such as overload costs. You can pay additional costs such as kicker costs. If the card has mandatory additional costs, you must pay those."
Quote from Snow-FurDumb question, but how does this react with Goblin Electromancer?
Quote from AquajoltElectromancer just reduces its cost by 1. If you pay UR for Epic Experiment you get to reveal 1 card (and hope its an instant or sorcery with CMC 1). If you pay 5UR, then you can reveal 6. Electromancer just reduces a colorless cost (1 ) from the total cost. Just announce what X equals to your opponenet noting the cost reduction from the Electromancer so everyone is on the same page.