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qid 7993 · math

Question: 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 $>y$ ).

  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. $0.01$

Our answer: C. $0.03$ Source quote machine-checked (exact quote)

A machine check confirms the quoted words appear at the source. A person has not yet reviewed these. EARN MARKS as a Human Reviewer

How it was answered

Stored method, replayed by code (kind: formula)

card: formula · card sha256 646a2b6a71504ba7…

Current source

Wikipedia, "Reliability block diagram"

https://en.wikipedia.org/wiki/Reliability_block_diagram

“For example, a group of parallel blocks could require two out of three components to succeed for the system to succeed. By contrast, any failure along a series path causes the entire series path to fail.”

Source quote machine-checked (exact quote)

retrieved 2026-09-18T01:16:52.651Z

page text sha256 14d66bba0db87e90… · content sha256 e5e5f0661a558ba9…

addendum formula_qid7993.formula_ADDENDUM_source_rs20260918T011652Z · sha256 e843c8e11565b810… · replaces the version below, addendum sha256 84209722a79e78f3…

Earlier version (superseded)

https://en.wikipedia.org/wiki/Weibull_distribution

Source weak (http_get_200_text_and_question_terms)

retrieved 2026-09-17T01:44:13.706Z

page text sha256 121eda18ecb334c4… · content sha256 —

addendum formula_qid7993.formula_ADDENDUM_source_bf20260917T014413Z · sha256 84209722a79e78f3… · replaces the version below, addendum sha256 c62de29925597964…

Earlier version (superseded)

No public source has been found for this card yet (2 places checked internally).

addendum formula_qid7993.formula_ADDENDUM_source · sha256 c62de29925597964…

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