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(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).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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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).
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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