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Just a quick question on interpreting what this pdf looks like:

Bacteria are distributed randomly and uniformly throughout river water at the rate of $\lambda$ bacteria per unit volume. n test tubes contain know volumes $v1,v2,...,vn$ of river water are prepared.

So I know it is uniform so the bacteria in each of the tubes is distributed as $uniform(b,a)$.

I guess that it is referring to concentration so $\frac{\lambda}{v_i}, i=1,...,n$ is the concentration in each tube then where do i fit that in with b and a

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    $\begingroup$ Hint: The presence of $\lambda$ and calling it the number of bacteria per unit volume makes me think about the Poisson. $\endgroup$ – Ertxiem Mar 31 at 2:21
  • $\begingroup$ @Ertxiem omm, but isn't poisson the number of events in a period of time so i would write $\frac{\lambda^{v_i}e^{-\lambda}}{v_i !}$ and $i=1,...,n$. And that isn't really about number of events happening $\endgroup$ – glockm15 Mar 31 at 2:44
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    $\begingroup$ Poisson does not need to be per period of time, and instead of number of events, I thought about number of bacteria. If the number of bacteria in each test tube is not too large (I would say, up to a few dozens) then the Poisson appears to be adequate to me. What is exactly the question you want to answer? $\endgroup$ – Ertxiem Mar 31 at 3:30
  • $\begingroup$ I don't think this is a Poisson type problem because there's no "rate". It's just a distribution of bacteria per unit volume, which we're explicitly told is uniform. Suppose instead of a lake, we had a flat 1x1 square, and we randomly (and uniformly) distribute 1000 bacteria in it. Then if we took a 0.5 x 0.5 square within that original square, we'd on average expect to get 25 bacteria in it. This sounds much more like a binomial count to me than a Poisson count $\endgroup$ – Bayesic Apr 1 at 14:07

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