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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
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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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
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
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