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The number of substance S in a water well (X) is a Poisson random variable with an expected value of 1 substance per liter.
As far as I know, values provided should be non-negative integers. However I am asked the following questions:

What are the values of P(-0.5 < X < 0.5) and P(1.5 < X < 2.5)?

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closed as unclear what you're asking by Xi'an, jbowman, Scortchi Apr 10 '18 at 19:45

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I have to assume that there is a count of some kind in some volume of water. Please provide the missing details. $\endgroup$ – JimB Apr 10 '18 at 18:43
  • $\begingroup$ @JimB I just rechecked, that is all the information that is provided. I added the word substance between 1 and per though. $\endgroup$ – Elia Apr 10 '18 at 19:11
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    $\begingroup$ Zero is between -0.5 and 0.5 Two is between 1.5 and 2.5. $\endgroup$ – The Laconic Apr 10 '18 at 19:20
  • $\begingroup$ @TheLaconic Do you mind expanding? $\endgroup$ – Elia Apr 10 '18 at 19:22
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    $\begingroup$ "Number of substance" doesn't make sense; but anyway, if the expected count is per litre, we need to know how many litres are in the well. $\endgroup$ – Scortchi Apr 10 '18 at 19:50
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X is Poisson. X can take only non-negative integer values. The only non-negative integer value in the interval (-0.5, 0.5) is zero. So $P(-0.5 < X < 0.5) = P(X=0)$, which you should be able to calculate. And similarly, $P(1.5 < X < 2.5) = P(X=2)$.

It's an oddly-phrased question. It's possible that it was intended to confuse you.

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  • $\begingroup$ Thank you, I wanted to do that but thought I was missing something. $\endgroup$ – Elia Apr 10 '18 at 20:00

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