# Poisson random variable with non-integer values [closed]

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)?

• I have to assume that there is a count of some kind in some volume of water. Please provide the missing details. – JimB Apr 10 '18 at 18:43
• @JimB I just rechecked, that is all the information that is provided. I added the word substance between 1 and per though. – Elia Apr 10 '18 at 19:11
• Zero is between -0.5 and 0.5 Two is between 1.5 and 2.5. – The Laconic Apr 10 '18 at 19:20
• @TheLaconic Do you mind expanding? – Elia Apr 10 '18 at 19:22
• "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. – 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, $P(1.5 < X < 2.5) = P(X=2)$.