(Note: It might take a while for the math symbols to load.)
In my previous post I set up the problem of gun statistics and planet statistics (where I mean math-problem, rather than trouble-problem). There's a question of the number of guns per capita, versus the fraction of the population with a gun (fraction of citizenry that are gun-owners). Also in there is the number of guns per gun-owner.
Similarly, there's the question of the number of planets per star throughout the galaxy, the fraction of stars with a planetary system, and the number of planets per system.
To illustrate this mathematically (and this involves nothing but multiplication and division, so stay with me!), let's set up two scenarios. Both scenarios have five stars and five planets:
Now let's introduce some mathematical terms. The first is the total number of stars in our sample, $N_\star$. Next is the number of planets, $n_p$. In both of the cases in the figure above, $n_p = 5$ and $N_\star = 5$. The…