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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    $\begingroup$ 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 - Reinstate Monica Apr 10 '18 at 19:50

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.

  • $\begingroup$ 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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