## 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

1. anonymous

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

2. anonymous

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

3. razor99

srry i am trying to grt help.

4. anonymous

Ok :)

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

But, why?

9. anonymous

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

10. anonymous

I didn't get that...

11. anonymous

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

12. anonymous

No...

13. anonymous

ok so now you know it :P :D

14. anonymous

Yes :)

15. anonymous

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

16. anonymous

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

17. 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

18. anonymous

so not put limits as 500 to infinity,

19. anonymous

Thanks so much!

20. anonymous

No problem....