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5. Suppose Y₁, Y2, ..., Y5 are mutually independent lug nut lifetimes. Assume each lug nut has probability density function (pdf) fy(y) = { 3y², 0

5. Suppose Y₁, Y2, ..., Y5 are mutually independent lug nut lifetimes. Assume each lug nut has probability density function (pdf) fy(y) = { 3y², 0

MATLAB: An Introduction with Applications
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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5. Suppose Y₁, Y2, ..., Y5 are mutually independent lug nut lifetimes. Assume each lug nut has probability density function (pdf) fy(y) = 3y², 0<y <1 0, otherwise. The lug nuts are arranged as a five-component engineering system. (a) If the lug nuts are arranged in a series system, then the lifetime of the system will be determined by Y(1) = min{Y₁, Y2, ..., Y5}, that is, the system will fail when the first lug nut fails. Find the pdf of Y(1). (b) If the lug nuts are arranged in a parallel system, then the lifetime of the system will be determined by Y(5) max{Y₁, Y2, ..., Y5}, that is, the system will fail when the last lug nut fails. Find the pdf of Y(5). (c) Find the pdf of the sample median Y(3) and calculate P(Y(3) > 0.5). =
Transcribed Image Text:5. Suppose Y₁, Y2, ..., Y5 are mutually independent lug nut lifetimes. Assume each lug nut has probability density function (pdf) fy(y) = 3y², 0<y <1 0, otherwise. The lug nuts are arranged as a five-component engineering system. (a) If the lug nuts are arranged in a series system, then the lifetime of the system will be determined by Y(1) = min{Y₁, Y2, ..., Y5}, that is, the system will fail when the first lug nut fails. Find the pdf of Y(1). (b) If the lug nuts are arranged in a parallel system, then the lifetime of the system will be determined by Y(5) max{Y₁, Y2, ..., Y5}, that is, the system will fail when the last lug nut fails. Find the pdf of Y(5). (c) Find the pdf of the sample median Y(3) and calculate P(Y(3) > 0.5). =
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