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Two Envelopes Two envelopes, each containing a check, are placed in front of you. You are to choose one of the envelopes, open it, and see the amount of the check. At this point you can either accept that amount or you can exchange it for the check in the unopened envelope. Your goal is to maximize your expected reward. Let A and B denote the (unknown) amount of the checks, and note that the strategy that randomly selects an envelope and always accepts its check has an "expected return" of (A+B)/2. Can you do better?

Two Envelopes Two envelopes, each containing a check, are placed in front of you. You are to choose one of the envelopes, open it, and see the amount of the check. At this point you can either accept that amount or you can exchange it for the check in the unopened envelope. Your goal is to maximize your expected reward. Let A and B denote the (unknown) amount of the checks, and note that the strategy that randomly selects an envelope and always accepts its check has an "expected return" of (A+B)/2. Can you do better?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Hi I want to get a detailed solution for this question

Two Envelopes Two envelopes, each containing a check, are placed in front of you. You are to choose one of the envelopes, open it, and see the amount of the check. At this point you can either accept that amount or you can exchange it for the check in the unopened envelope. Your goal is to maximize your expected reward. Let A and B denote the (unknown) amount of the checks, and note that the strategy that randomly selects an envelope and always accepts its check has an "expected return" of (A+B)/2. Can you do better? Wharton Tony Cai 9
Transcribed Image Text:Two Envelopes Two envelopes, each containing a check, are placed in front of you. You are to choose one of the envelopes, open it, and see the amount of the check. At this point you can either accept that amount or you can exchange it for the check in the unopened envelope. Your goal is to maximize your expected reward. Let A and B denote the (unknown) amount of the checks, and note that the strategy that randomly selects an envelope and always accepts its check has an "expected return" of (A+B)/2. Can you do better? Wharton Tony Cai 9
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