This paper presents the following two envelopes problem: imagine that you have two envelopes in front of you, one of them contains amount x and the other one 2x. We randomly choose one and look at the content. Now we have to decide, whether we want to stay with the chosen envelope or switch to the other one. The thesis is divided into six main sections. In the first section we present the problem and we give a more detailed history of the problem and present some other variations of the problem. In the main part of the thesis, the second, third and forth chapter we derivate General Exchange Condition, Exchange Condition for discrete distributions and Exchange Condition for continuous distributions. We also apply the conditions on some examples and show, that they always work for at least some of the values, if not all. In the fifth section we take a look at the utilities concept, where the gain in the envelope is not measured in money. In the sixth section we look at some strategies, that can be useful in solving the problem and compare them.
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