A hole is drilled in a sheet-metal component, and then a shaft is inserted through the hole. The shaft clearance is equal to the difference between the radius of the hole and the radius of the shaft. Let the random variable X denote the clearance, in millimeters. Assume that the probability density function of X is: fx(x) = { 1.25 (1 – x*) if 0 < x < 1 otherwise - Components with clearances larger than 0.8 mm must be scrapped. a) What proportion of components are scrapped? b) Find the cumulative distribution function of X and use it to determine the probability that the shaft clearance is less than 0.5 mm. c) Find the mean and variance of the clearance.
A hole is drilled in a sheet-metal component, and then a shaft is inserted through the hole. The shaft clearance is equal to the difference between the radius of the hole and the radius of the shaft. Let the random variable X denote the clearance, in millimeters. Assume that the probability density function of X is: fx(x) = { 1.25 (1 – x*) if 0 < x < 1 otherwise - Components with clearances larger than 0.8 mm must be scrapped. a) What proportion of components are scrapped? b) Find the cumulative distribution function of X and use it to determine the probability that the shaft clearance is less than 0.5 mm. c) Find the mean and variance of the clearance.
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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Transcribed Image Text:A hole is drilled in a sheet-metal component, and then a shaft is inserted through the hole.
The shaft clearance is equal to the difference between the radius of the hole and the radius of
the shaft. Let the random variable X denote the clearance, in millimeters. Assume that the
probability density function of X is:
fx(x) = {1.25 (1 – x*) if0<x <1
otherwise
-
Components with clearances larger than 0.8 mm must be scrapped.
a) What proportion of components are scrapped?
b) Find the cumulative distribution function of X and use it to determine the probability that
the shaft clearance is less than 0.5 mm.
c) Find the mean and variance of the clearance.
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