Consider the following question as example.
When biking to school you have an average of 2 flat tires a year. What is the chance of having to flat tires in one month?
I know how I'd use the Poisson Distribution to calculate the probability of zero of five flat tires, using the following Python code:
x = range(0, 5)
r = stats.poisson.pmf(x, 2)
print(r)
However, how would I calculate it for a month? I tried reasoning that I should multiple the 2 with 12 because there are 12 months in a year but that did not give the desired result of 0,01176. I have no clue on how to do this...
Since a month is one-twelfth as long as a year, your Poisson parameter for a month's worth of flat tires should be $\lambda_{\rm month}=\frac{2}{12}$, rather than $2\cdot 12$.