(a) A lamp has two bulbs, each of a type with average lifetime 1,700 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function with mean ? = 1,700, find the probability that both of the lamp's bulbs fail within 1,700 hours. (Round your answer to four decimal places.) (b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1,700 hours. (Round your answer to four decimal places.)
(a) A lamp has two bulbs, each of a type with average lifetime 1,700 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function with mean ? = 1,700, find the probability that both of the lamp's bulbs fail within 1,700 hours. (Round your answer to four decimal places.) (b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1,700 hours. (Round your answer to four decimal places.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
(a)
A lamp has two bulbs, each of a type with average lifetime 1,700 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function with mean ? = 1,700, find the probability that both of the lamp's bulbs fail within 1,700 hours. (Round your answer to four decimal places.)
(b)
Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1,700 hours. (Round your answer to four decimal places.)
Transcribed Image Text:**Problem Statement:**
(a) A lamp has two bulbs, each of a type with average lifetime 1,700 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function with mean \( \mu = 1,700 \), find the probability that both of the lamp's bulbs fail within 1,700 hours. (Round your answer to four decimal places.)
- Answer: 0.3996 ✔
(b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1,700 hours. (Round your answer to four decimal places.)
- Answer: 0.4180 ✖
**Explanation of Diagrams:**
There are no graphs or diagrams provided in this problem. The question involves calculations based on the exponential distribution of bulb lifetimes.
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