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Test exercise, year 2010, December 23

An electronic company notes that the number of components failing before reaching 100 hours of operation is a Poisson random variable. If the average number of these faults is eight:

  1. What is the probability that a component will fail in 25 hours?
  2. What is the probability that no more than two components fail within 50 hours?
  3. What is the probability that they will fail at least ten in 125 hours?

Let X be the number of components that fail per hour with mean $λ=8/100=0.08$

  1. $25λ=2\Rightarrow P(X=1)=0.2707$
  2. $50λ=4\Rightarrow P(X≤2)=0.2381$
  3. $125λ=10\Rightarrow$ According to the teacher $P(X>10)=1-P(<10)$, why?

Thank you very much.

  • 4
    3 should be $P(X\geq10)=1-P(X<10)$ – 2017-02-27
  • 1
    @AlexR. And finally $1-P(X<10)=1-P(X≤9)$? – 2017-02-27
  • 0
    yes, that's right – 2017-03-01

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