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

Question

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 · Answer

$$\int\limits_{400}^{\infty} kx^{-2}$$

How do you do this to get an answer as 400?

anonymous · Answer

it's $$x \ge 400 $$otherwise..

razor99 · Answer

srry i am trying to grt help.

anonymous · Answer

Ok :)

anonymous · Answer

$$\int\limits_{0}^{\infty} kx ^{-2} =1$$ . This does not seem to give the answer. Are you sure the question is typed correctly?

anonymous · Answer

It's 400 at the bottom... I changed it underneath the question

anonymous · Answer

ok then that integral is just k/400=1.
k=400.

anonymous · Answer

But, why?

anonymous · Answer

$$\int\limits_{400}^{\infty}kx ^{-2}= -k/x$$ put limits 1/infinity is 0 substitue 400 you'll get the answer.

anonymous · Answer

I didn't get that...

anonymous · Answer

integral of x^a is x^(a+1)/(a+1) do you know that?

anonymous · Answer

No...

anonymous · Answer

ok so now you know it :P :D

anonymous · Answer

Yes :)

anonymous · Answer

I did know it, sorry... So what then?

anonymous · Answer

Here a=-2 you get -1/x as the integral which on putting limits becomes 1/400.

anonymous · Answer

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 · Answer

so not put limits as 500 to infinity,

anonymous · Answer

Thanks so much!

anonymous · Answer

No problem....