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 twiceandobtain numbers X1 and X2.(a) Calculate E(max(X₁, X2)) and E(min(X₁, X2)).(b) Show that your calculation in part (a) verifies thatE(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 ofit?

(a) Since the die is fair, each of the numbers 1,2,…,n has an equal probability of 1n of appearing…

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?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

See similar textbooks