The length of life Y for fuses of a certain type is modeled by the exponential distribution, with f(y) = e-y/3 3 0, y > 0, elsewhere. (The measurements are in hundreds of hours.) (a) If two such fuses have independent lengths of life Y, and Y₂, find the joint probability density function for Y₁ and Y₂. f(y₁, y₂) = , where y₁ > Y₂> (b) One fuse in part (a) is in a primary system, and the other is in a backup system that comes into use only if the primary system fails. The total effective length of life of the two fuses is then Y₁ + Y₂. Find P(Y₁ + Y₂ S 8). (Round your answer to four decimal places.)
The length of life Y for fuses of a certain type is modeled by the exponential distribution, with f(y) = e-y/3 3 0, y > 0, elsewhere. (The measurements are in hundreds of hours.) (a) If two such fuses have independent lengths of life Y, and Y₂, find the joint probability density function for Y₁ and Y₂. f(y₁, y₂) = , where y₁ > Y₂> (b) One fuse in part (a) is in a primary system, and the other is in a backup system that comes into use only if the primary system fails. The total effective length of life of the two fuses is then Y₁ + Y₂. Find P(Y₁ + Y₂ S 8). (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
Related questions
Question
Transcribed Image Text:The length of life Y for fuses of a certain type is modeled by the exponential distribution, with
- fom
f(y)
e-y/3, y> 0,
elsewhere.
(The measurements are in hundreds of hours.)
(a) If two such fuses have independent lengths of life Y₁ and Y₂, find the joint probability density function for Y₁ and Y₂.
f(y₁ y ₂) =
, where y₁ >
Y2>
(b) One fuse in part (a) is in a primary system, and the other is in a backup system that comes into use only if the primary system fails. The total effective length of life of
the two fuses is then Y₁ + Y₂. Find P(Y₁ + Y₂ ≤ 8). (Round your answer to four decimal places.) 4
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Similar questions
- Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
