I am stuck with a statistics problem based on exponential distribution, can anyone help?

Question

anonymous · Answer

Hey Arjun - maybe... What's your problem?

anonymous · Answer

Post the problem i might be able to help out

anonymous · Answer

Thanks for the response folks. The problem is:
After given an antibiotic in dogs, certain type of bacteria dies completely within six to twelve hours based on an exponential distribution; i.e. f(x) = 0.95 e ^{-x/3}., where $$6\le x \le$$ . What is the probability that a dog receiving the antibiotic will be completely free of bacteria in less than eight hours?

anonymous · Answer

x is greater than and equal to 6, and x is less than and equal to 12

waheguru · Answer

wow hard

anonymous · Answer

you could integrate the function and evaluate first on the interval 6 to 12 and then from 6 to 8. and do the following:$$\int\limits_{6}^{8}f(x) \div \int\limits_{6}^{12}f(x)$$
it's just a thought, i'm not entirely sure

anonymous · Answer

Thanks estebananaya, m not too completely sure but trying right now

turingtest · Answer

I knew Zarkon would shoot over here.
I'm posting so I can see the solution if you get it.

anonymous · Answer

Well that would be great if Zarkon can figure this out..

zarkon · Answer

the pdf you gave doesn't integrate to 1.

anonymous · Answer

so, do you think there is a typo in question.. I tried estebananaya's way (posted above) and it came down to .25, but not sure if its right..

zarkon · Answer

if $f$ is a true pdf then it is required that 

$$\int_{\Omega}f(x)dx=1$$

where $\Omega$ is the support of the distribution

anonymous · Answer

well, no doubts about that.. and one other way I see it, is to subtract individual probabilities, I mean calculating at 8 and 6, and subtracting.. but not sure..

zarkon · Answer

I would double check the problem to make sure you have typed it correctly.  If you have typed it correctly then the problem is ill posed since they didn't give you a true density function

anonymous · Answer

Zarkon, in question there is an incomplete equation for x, it has to be $$6\le x \le12$$

zarkon · Answer

for your $f$

$$\int\limits_{6}^{12}f(x)dx\ne 1$$

anonymous · Answer

thanks