benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 7993 / 5.3-13. A device contains three components, each of which has a lifetime in…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

5.3-13. A device contains three components, each of which has a lifetime in hours with the pdf f(x)=2x102e−(x/10)2,0<x<∞. f(x)=\frac{2 x}{10^2} e^{-(x / 10)^2}, \quad 0 < x < \infty . The device fails with the failure of one of the components. Assuming independent lifetimes, what is the probability that the device fails in the first hour of its operation? HINT: G(y)=P(Y≤y)=1−P(Y>y)=1−PG(y)=P(Y \leq y)=1-P(Y>y)=1-P (all three >y>y ).
Plain-text mathematical notation (without MathML)
5.3-13. A device contains three components, each of which has a lifetime in hours with the pdf
f(x)=(2x)/(10²)e^(−(x/10)²), 0<x<∞.
The device fails with the failure of one of the components. Assuming independent lifetimes, what is the probability that the device fails in the first hour of its operation? HINT: G(y)=P(Y≤y)=1−P(Y>y)=1−P (all three >y ).
Original LaTeX notation
5.3-13. A device contains three components, each of which has a lifetime in hours with the pdf
$$
f(x)=\frac{2 x}{10^2} e^{-(x / 10)^2}, \quad 0 < x < \infty .
$$
The device fails with the failure of one of the components. Assuming independent lifetimes, what is the probability that the device fails in the first hour of its operation? HINT: $G(y)=P(Y \leq y)=1-P(Y>y)=1-P$ (all three $>y$ ).

category

math

options

  1. $0.08$
  2. $0.04$
  3. $0.03$
  4. $0.05$
  5. $0.06$
  6. $0.02$
  7. $0.10$
  8. $0.07$
  9. $0.09$
  10. $0.01$

src

scibench-stat

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
7993
task_id
48c7f9f4-71ef-5751-95a3-cb1f6f3f3ab1
task_key
default--test--7993
task_revision_id
1
config / split
default / test

Official source

initial import