If i know an average such as ( catch an average of one rat every 39 minutes ) what is the average number of rats caught in 10 hours ?
is it as simple as dividing 600/39 (600 = 10 hours in minutes) and multiplying this value by number of rats caught in 39 minutes ?
in this case 15.38 rats caught in 10 hours.
Graphical comment. Suppose rat catching is at random so that the number $X$ of rats caught in 10 hours is distributed as $\mathsf{Pois}(\lambda = 15.3846).$ Then, according to @ATF's computation, the probabilities $P(X = x),$ for $x=0, 1, \dots, 40$ can be plotted in R as follows:
x = 0:40; lam = 15.3846
PDF = dpois(x, lam)
plot(x, PDF, type="h", lwd=2, col="blue", main="PDF of POIS(15.3846)")
abline(h = 0, col="green2"); abline(v = 0, col="green2")
Only rarely, would one catch fewer than 5 or more than 30 rats in 20 hours.
