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.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....

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