A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
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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A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed
with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first
bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes
of the bulbs are independent.
![a) Find P X >
100]
b) Find P X > 100 n X2 > 100 n
.. n X3 > 100|
c) Explain why the event (T > 100) is the same as (X1 > 100 n X2 > 100 N . n X; >
100)
d) Let t be any positive number. Find P T < t , which is the cumulative distribution function
of T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ea15aad-ce09-44c1-ae1a-fd69c581a5af%2F009879d4-fe6e-43ba-8ce0-b41e91e3cce8%2Fo8w4oeb_processed.png&w=3840&q=75)
Transcribed Image Text:a) Find P X >
100]
b) Find P X > 100 n X2 > 100 n
.. n X3 > 100|
c) Explain why the event (T > 100) is the same as (X1 > 100 n X2 > 100 N . n X; >
100)
d) Let t be any positive number. Find P T < t , which is the cumulative distribution function
of T.
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