A system consisting of two components will con- tinue to operate only as long as both components function. Suppose the joint pdf of the lifetimes (months) of the two components in a system is given by f(x, y) = c[10 - (x+y) for x > 0, y > 0, x+ y < 10 a. If the first component functions for exactly 3 months, what is the probability that the sec- ond functions for more than 2 months? b. Suppose the system will continue to work only as long as both components function. Among 20 of these systems that operate independently of each other, what is the probability that at least half work for more than 3 months?

A system consisting of two components will con- tinue to operate only as long as both components function. Suppose the joint pdf of the lifetimes (months) of the two components in a system is given by f(x, y) = c[10 - (x+y) for x > 0, y > 0, x+ y < 10 a. If the first component functions for exactly 3 months, what is the probability that the sec- ond functions for more than 2 months? b. Suppose the system will continue to work only as long as both components function. Among 20 of these systems that operate independently of each other, what is the probability that at least half work for more than 3 months?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 35EQ

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Question

A system consisting of two components will con-
tinue to operate only as long as both components
function. Suppose the joint pdf of the lifetimes
(months) of the two components in a system
is given by f(x, y) = c[10 – (x+ y)] for x > 0,
y > 0, x+y < 10
a. If the first component functions for exactly
3 months, what is the probability that the sec-
ond functions for more than 2 months?
b. Suppose the system will continue to work only
as long as both components function. Among 20
of these systems that operate independently of
each other, what is the probability that at least
half work for more than 3 months?

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