anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\int\limits_{400}^{\infty} kx^{-2}\] How do you do this to get an answer as 400?
anonymous
  • anonymous
it's \[x \ge 400 \]otherwise..
razor99
  • razor99
srry i am trying to grt help.

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anonymous
  • anonymous
Ok :)
anonymous
  • anonymous
\[\int\limits_{0}^{\infty} kx ^{-2} =1\] . This does not seem to give the answer. Are you sure the question is typed correctly?
anonymous
  • anonymous
It's 400 at the bottom... I changed it underneath the question
anonymous
  • anonymous
ok then that integral is just k/400=1. k=400.
anonymous
  • anonymous
But, why?
anonymous
  • anonymous
\[\int\limits_{400}^{\infty}kx ^{-2}= -k/x\] put limits 1/infinity is 0 substitue 400 you'll get the answer.
anonymous
  • anonymous
I didn't get that...
anonymous
  • anonymous
integral of x^a is x^(a+1)/(a+1) do you know that?
anonymous
  • anonymous
No...
anonymous
  • anonymous
ok so now you know it :P :D
anonymous
  • anonymous
Yes :)
anonymous
  • anonymous
I did know it, sorry... So what then?
anonymous
  • anonymous
Here a=-2 you get -1/x as the integral which on putting limits becomes 1/400.
anonymous
  • anonymous
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
anonymous
  • anonymous
so not put limits as 500 to infinity,
anonymous
  • anonymous
Thanks so much!
anonymous
  • anonymous
No problem....

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