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5.15 The weekly repaik cost, X, for a certain machine has a probability density function given by 6x(1 - x), 0

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

DISImbononS
5.15 The weekly repaik cost, X, for a certain machine has a probability density function given by
бх(1 — х), 0<x<1
done-
f (x) =
0,
otherwise
0.75°
with measurements in $100s.'
a
Find the mean and variance of the distribution of repair costs.
b Find an interval within which these weekly repair costs should lie at least 75% of the time using
Tchebysheff's Theorem.
Find an interval within which these weekly repair costs lie exactly 75% of the time with exactly
half of those not lying in the interval above the upper limit and the other half below the lower
limit. Compare this interval to the one obtained in part (b).

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