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A lamp has 3 light bulbs. Each lightbulb has a life span that corresponds to a random variable X, for i = 1, 2, 3, measured in hours, with pdf given as e-*/2000 = {} 0 fx (x) = 2000 x>0 x≤0 Assume that all the lightbulbs are independent. Lightbulbs are not replaced until all of them stop working. Find the probability that the lamp will work less than 1,500 hours. O (1-e-3/4)3 O (1-e-1/2)3 01-(1-e-3/4)3 01-(1-e-¹/2)³

A lamp has 3 light bulbs. Each lightbulb has a life span that corresponds to a random variable X, for i = 1, 2, 3, measured in hours, with pdf given as e-*/2000 = {} 0 fx (x) = 2000 x>0 x≤0 Assume that all the lightbulbs are independent. Lightbulbs are not replaced until all of them stop working. Find the probability that the lamp will work less than 1,500 hours. O (1-e-3/4)3 O (1-e-1/2)3 01-(1-e-3/4)3 01-(1-e-¹/2)³

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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A lamp has 3 light bulbs. Each lightbulb has a life span that corresponds to a random variable X, for i = 1, 2, 3, measured in hours, with pdf given as e-*/2000 fx (a) = {} 0 2000 O (1-e-3/4)3 O (1-e-1/2)3 Assume that all the lightbulbs are independent. Lightbulbs are not replaced until all of them stop working. Find the probability that the lamp will work less than 1,500 hours. x>0 x≤0 01-(1-e-3/4)3 01-(1-e-¹/2)³
Transcribed Image Text:A lamp has 3 light bulbs. Each lightbulb has a life span that corresponds to a random variable X, for i = 1, 2, 3, measured in hours, with pdf given as e-*/2000 fx (a) = {} 0 2000 O (1-e-3/4)3 O (1-e-1/2)3 Assume that all the lightbulbs are independent. Lightbulbs are not replaced until all of them stop working. Find the probability that the lamp will work less than 1,500 hours. x>0 x≤0 01-(1-e-3/4)3 01-(1-e-¹/2)³
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