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Rolling a fair n-sided die gives us a random number uniformly distributed among {1, 2,..., n} (our usual die is n = 6). Suppose we independently roll a fair n-sided die twice andobtain numbers X1 and X2. (a) Calculate E(max(X₁, X₂)) and E(min(X₁, X2)). (b) Show that your calculation in part (a) verifies that E(max(X₁, X2)) + E(min(X₁, X2)) = E(X₁) + E(X₂). (c) Is the above equation simply a coincidence? Can you give a simple and direct proof of it?

Rolling a fair n-sided die gives us a random number uniformly distributed among {1, 2,..., n} (our usual die is n = 6). Suppose we independently roll a fair n-sided die twice andobtain numbers X1 and X2. (a) Calculate E(max(X₁, X₂)) and E(min(X₁, X2)). (b) Show that your calculation in part (a) verifies that E(max(X₁, X2)) + E(min(X₁, X2)) = E(X₁) + E(X₂). (c) Is the above equation simply a coincidence? Can you give a simple and direct proof of it?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Rolling a fair n-sided die gives us a random number uniformly distributed among {1,2,..., n} (our usual die is n = 6). Suppose we independently roll a fair n-sided die twice andobtain numbers X1 and X2. (a) Calculate E(max(X₁, X2)) and E(min(X₁, X2)). (b) Show that your calculation in part (a) verifies that E(max(X1, X2)) + E(min(X₁, X2)) = E(X1) + E(X₂). (c) Is the above equation simply a coincidence? Can you give a simple and direct proof of it?
Transcribed Image Text:Rolling a fair n-sided die gives us a random number uniformly distributed among {1,2,..., n} (our usual die is n = 6). Suppose we independently roll a fair n-sided die twice andobtain numbers X1 and X2. (a) Calculate E(max(X₁, X2)) and E(min(X₁, X2)). (b) Show that your calculation in part (a) verifies that E(max(X1, X2)) + E(min(X₁, X2)) = E(X1) + E(X₂). (c) Is the above equation simply a coincidence? Can you give a simple and direct proof of it?
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