Page "Parameter" Paragraph 36

For instance, suppose we have a radioactive sample that emits, on average, five particles every ten minutes.

We take measurements of how many particles the sample emits over ten-minute periods.

The measurements will exhibit different values of k, and if the sample behaves according to Poisson statistics, then each value of k will come up in a proportion given by the probability mass function above.

From measurement to measurement, however, λ remains constant at 5.

If we do not alter the system, then the parameter λ is unchanged from measurement to measurement ; if, on the other hand, we modulate the system by replacing the sample with a more radioactive one, then the parameter λ would increase.