Statistics: a very brief interlude

Dear Readers,

welcome again for a new, exciting (?), one minute physics session! Together, we went through the definition of UPC physics. We saw the photon, the Pomeron, the Feynman diagram.

I heavily suspect that you all have a question:

What is the point of UPC? Why are physicists studying them?

Well, a few theorists would likely reply:

Because they are beautiful…

While this is certainly true, it is obviously not the end of the story… This will be a long reply, and I will divide it in a few consecutive posts. Please, send me a mail at simone.ragoni.94@gmail.com in case of questions. In addition, my UPC Seniors and Advisors would certainly be very much willing to reply to every question. They are people I greatly admire, and their replies would be complete and exhaustive.

Anyway, the key concept in my opinion comes from statistics. In statistics, there is something called probability. I believe everyone has heard of it. However, usually we deal with discrete probability. What this means will become clear now:

We have two dice. Two beautiful six faced dice, not one of those weird things like a d20 people use to play at D&D (Dungeons and Dragons, I am terrible at it…). Now, you want to compute the probability that the sum of the faces once you have thrown them is: two, three, four, five, six and so on. You are hence computing something like a discrete probability function, although my professors would certainly disapprove of me calling it like this. But my motto is that if it works, it works (the real problems come when things just do not work…).

Now, we want to generalise the concept. Instead of unit jumps (from two to three and then four and five), we have infinitesimally small increases. We can assign a number to them. Then, we basically have a continuous function. We can compute the area under the curve.

If it is one, then we have a probability density function! Hurray!