6. One hundred numbers are rounded to the nearest integer and then added to- gether. Assuming round-off errors are independent and identically distributed as Unif(-1/2, 1/2) random variables, use the Central Limit Theorem to show that there is about a 27% chance that the sum of the rounded numbers and the sum of unrounded numbers will differ by at most 1.
6. One hundred numbers are rounded to the nearest integer and then added to- gether. Assuming round-off errors are independent and identically distributed as Unif(-1/2, 1/2) random variables, use the Central Limit Theorem to show that there is about a 27% chance that the sum of the rounded numbers and the sum of unrounded numbers will differ by at most 1.
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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Transcribed Image Text:6. One hundred numbers are rounded to the nearest integer and then added to-
gether. Assuming round-off errors are independent and identically distributed
as Unif(-1/2, 1/2) random variables, use the Central Limit Theorem to show
that there is about a 27% chance that the sum of the rounded numbers and the
sum of unrounded numbers will differ by at most 1.
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