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anonymous

  • 4 years ago

A computer ink cartridge has a life of X hours. The variable X is modelled by the probability density function \[f(x)=\left(\begin{matrix}kx^{-2} \\ 0\end{matrix}\right)\]x ≥ 0 otherwise (a) Find K

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  1. anonymous
    • 4 years ago
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    \[\int\limits_{400}^{\infty} kx^{-2}\] How do you do this to get an answer as 400?

  2. anonymous
    • 4 years ago
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    it's \[x \ge 400 \]otherwise..

  3. razor99
    • 4 years ago
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    srry i am trying to grt help.

  4. anonymous
    • 4 years ago
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    Ok :)

  5. anonymous
    • 4 years ago
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    \[\int\limits_{0}^{\infty} kx ^{-2} =1\] . This does not seem to give the answer. Are you sure the question is typed correctly?

  6. anonymous
    • 4 years ago
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    It's 400 at the bottom... I changed it underneath the question

  7. anonymous
    • 4 years ago
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    ok then that integral is just k/400=1. k=400.

  8. anonymous
    • 4 years ago
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    But, why?

  9. anonymous
    • 4 years ago
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    \[\int\limits_{400}^{\infty}kx ^{-2}= -k/x\] put limits 1/infinity is 0 substitue 400 you'll get the answer.

  10. anonymous
    • 4 years ago
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    I didn't get that...

  11. anonymous
    • 4 years ago
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    integral of x^a is x^(a+1)/(a+1) do you know that?

  12. anonymous
    • 4 years ago
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    No...

  13. anonymous
    • 4 years ago
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    ok so now you know it :P :D

  14. anonymous
    • 4 years ago
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    Yes :)

  15. anonymous
    • 4 years ago
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    I did know it, sorry... So what then?

  16. anonymous
    • 4 years ago
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    Here a=-2 you get -1/x as the integral which on putting limits becomes 1/400.

  17. anonymous
    • 4 years ago
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    Ah Ok. I see now :) Thanks. And there's a B part... (b) find the probability that such a cartridge has a life of at least 500 hours

  18. anonymous
    • 4 years ago
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    so not put limits as 500 to infinity,

  19. anonymous
    • 4 years ago
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    Thanks so much!

  20. anonymous
    • 4 years ago
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    No problem....

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