The Two Envelope Problem

Problem Statement#

The Question#

Interview question: Two envelopes sit in front of you. One contains twice as much money as the other, but you don't know which is which. You pick one at random, open it, and see the amount $X$ inside. You can either keep your envelope or switch to the other one. Should you switch?

This problem shows up at Jane Street, Citadel, and DE Shaw, typically in early-round i...