Answered: The weekly repair cost, X, for a…

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The weekly repair 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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

5.15 The weekly repair cost, X, for a certain machine has a probability density function given by
6x(1 – x), 0<x<1
0 <x<
f (x) =
0,
otherwise
with measurements in $100s.
D.
Find the mean and variance of the distribution of repair costs.
q.
Find an interval within which these weekly repair costs should lie at least 75% of the time using
Tchebysheff's Theorem.
C 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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