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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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 11CYU
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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? 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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