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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
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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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{400}^{\infty} kx^{2}\] How do you do this to get an answer as 400?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0it's \[x \ge 400 \]otherwise..

razor99
 4 years ago
Best ResponseYou've already chosen the best response.0srry i am trying to grt help.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{\infty} kx ^{2} =1\] . This does not seem to give the answer. Are you sure the question is typed correctly?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0It's 400 at the bottom... I changed it underneath the question

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok then that integral is just k/400=1. k=400.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{400}^{\infty}kx ^{2}= k/x\] put limits 1/infinity is 0 substitue 400 you'll get the answer.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0integral of x^a is x^(a+1)/(a+1) do you know that?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so now you know it :P :D

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I did know it, sorry... So what then?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Here a=2 you get 1/x as the integral which on putting limits becomes 1/400.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ah 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
 4 years ago
Best ResponseYou've already chosen the best response.0so not put limits as 500 to infinity,
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