<P> For example, the probability that it lives longer than 5 hours, but shorter than (5 hours + 1 nanosecond), is (2 hour) × (1 nanosecond) ≃ 6 × 10 (using the unit conversion 3.6 × 10 nanoseconds = 1 hour). </P> <P> There is a probability density function f with f (5 hours) = 2 hour . The integral of f over any window of time (not only infinitesimal windows but also large windows) is the probability that the bacterium dies in that window . </P> <P> A probability density function is most commonly associated with absolutely continuous univariate distributions . A random variable X has density f, where f is a non-negative Lebesgue - integrable function, if: </P> <Dl> <Dd> Pr (a ≤ X ≤ b) = ∫ a b f X (x) d x . (\ displaystyle \ Pr (a \ leq X \ leq b) = \ int _ (a) ^ (b) f_ (X) (x) \, dx .) </Dd> </Dl>

What does the distribution of a variable tell us