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An accountant wants to simplify his bookkeeping by rounding amounts to the nearest integer, for example, rounding $ 99.53 and $ 100.46 both to $100. What is the cumulative effect of this if there are, say, 100 amounts? To study this we model the rounding errors by 100 independent U (-0.5, 0.5) random variables X1, X2,..., X100. a) Compute the expectation and the variance of the Xi. b) Use Chebyshev's inequality to compute an upper bound for the probability P( |X1 + X2 + + X100 |> 10) that the cumulative rounding error X1 + X2 + ...+ X100 exceeds $10.

An accountant wants to simplify his bookkeeping by rounding amounts to the nearest integer, for example, rounding $ 99.53 and $ 100.46 both to $100. What is the cumulative effect of this if there are, say, 100 amounts? To study this we model the rounding errors by 100 independent U (-0.5, 0.5) random variables X1, X2,..., X100. a) Compute the expectation and the variance of the Xi. b) Use Chebyshev's inequality to compute an upper bound for the probability P( |X1 + X2 + + X100 |> 10) that the cumulative rounding error X1 + X2 + ...+ X100 exceeds $10.

A First Course in Probability (10th Edition)
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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2. An accountant wants to simplify his bookkeeping by rounding amounts to the nearest integer, for example, rounding $ 99.53 and $ 100.46 both to $100. What is the cumulative effect of this if there are, say, 100 amounts? To study this we model the rounding errors by 100 independent U (-0.5, 0.5) random variables X1, X2,..., X100. a) Compute the expectation and the variance of the Xi. b) Use Chebyshev's inequality to compute an upper bound for the probability P( |X1 + X2 + + X100 |> 10) that the cumulative rounding error X1 + X2 + ... + X100 exceeds $10.
Transcribed Image Text:2. An accountant wants to simplify his bookkeeping by rounding amounts to the nearest integer, for example, rounding $ 99.53 and $ 100.46 both to $100. What is the cumulative effect of this if there are, say, 100 amounts? To study this we model the rounding errors by 100 independent U (-0.5, 0.5) random variables X1, X2,..., X100. a) Compute the expectation and the variance of the Xi. b) Use Chebyshev's inequality to compute an upper bound for the probability P( |X1 + X2 + + X100 |> 10) that the cumulative rounding error X1 + X2 + ... + X100 exceeds $10.
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