(a) Let C denote the time when the room goes dark. Find the pdf of C. b) What is E[C]? Hint: the pdf you obtain in part (a) should be of a familiar type. (c) Suppose light bulb B burns out first. You then move light bulb A to another room, where it is the only bulb. Starting at the time it is turned on in the new room, what is the expected lifetime of bulb A in the new room? Hint: this question can be answered independently of parts (a) and (b).
(a) Let C denote the time when the room goes dark. Find the pdf of C. b) What is E[C]? Hint: the pdf you obtain in part (a) should be of a familiar type. (c) Suppose light bulb B burns out first. You then move light bulb A to another room, where it is the only bulb. Starting at the time it is turned on in the new room, what is the expected lifetime of bulb A in the new room? Hint: this question can be answered independently of parts (a) and (b).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 72E
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Question
Please help answer this practice problem
![A room is lit by two light bulbs which are connected in a series circuit. If either
light bulb fails, the room will go dark.
Let A and B denote the lifetimes (in years) of these two light bulbs. Assume that A~ Exp(2),
that B Exp(3), and that A and B are independent of each other.¹
(a) Let C denote the time when the room goes dark. Find the pdf of C.
(b) What is E[C]?
Hint: the pdf you obtain in part (a) should be of a familiar type.
(c) Suppose light bulb B burns out first. You then move light bulb A to another room,
where it is the only bulb.
Starting at the time it is turned on in the new room, what is the expected lifetime of
bulb A in the new room?
Hint: this question can be answered independently of parts (a) and (b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc012e98d-11f3-4ebf-9e91-31a87ace6c91%2Fe124d9ea-f23c-4a4e-899f-49ec2d5c3f9b%2Fpb06w8_processed.png&w=3840&q=75)
Transcribed Image Text:A room is lit by two light bulbs which are connected in a series circuit. If either
light bulb fails, the room will go dark.
Let A and B denote the lifetimes (in years) of these two light bulbs. Assume that A~ Exp(2),
that B Exp(3), and that A and B are independent of each other.¹
(a) Let C denote the time when the room goes dark. Find the pdf of C.
(b) What is E[C]?
Hint: the pdf you obtain in part (a) should be of a familiar type.
(c) Suppose light bulb B burns out first. You then move light bulb A to another room,
where it is the only bulb.
Starting at the time it is turned on in the new room, what is the expected lifetime of
bulb A in the new room?
Hint: this question can be answered independently of parts (a) and (b).
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