How is the popularity of a WebPage $($or of Instagram accounts, people, scientific works, etc$)$ calculated? A simple solution is to count how many times it is referenced by other pages. However, this is easy to cheat: one could just create millions of pages that reference a given page. A better idea is to say that a page is popular if it is referenced by popular pages. You may notice that this is a circular definition! However, there are ways to make this precise. For instance, the famous algorithm PageRank that made Google founders Sergey Brin and Larry Page famous $($and fabulously rich$)$ usyes this idea.

In this exercise consider a very simple model with three pages P$1,$ P$2,$ P$3,$ where

P$1$ references P$2$ only;