This exercise asks you to (partly) verify that linearity of expectation holds even of the random variables are not independent. Consider two 6-sided dice that are rolled independently. What is the expected value of the sum? Now consider the case where the first die is rolled normally and then the second die is set equal to the value shown on the first die. What is the expected value of the sum? Now consider the case where the first die is rolled normally and the second die is set equal to 7 minus the value of the first die. What is the expected value of the sum?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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This exercise asks you to (partly) verify that linearity of expectation holds even
if the random variables are not independent. Consider two 6-sided dice that are
rolled independently. What is the expected value of the sum? Now consider the
case where the first die is rolled normally and then the second die is set equal to the
value shown on the first die. What is the expected value of the sum? Now consider
the case where the first die is rolled normally and the second die is set equal to 7
minus the value of the first die. What is the expected value of the sum?
Transcribed Image Text:This exercise asks you to (partly) verify that linearity of expectation holds even if the random variables are not independent. Consider two 6-sided dice that are rolled independently. What is the expected value of the sum? Now consider the case where the first die is rolled normally and then the second die is set equal to the value shown on the first die. What is the expected value of the sum? Now consider the case where the first die is rolled normally and the second die is set equal to 7 minus the value of the first die. What is the expected value of the sum?
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