Problem Set 1

1. example: Find the most probable path that to spell "ray".

   After reading the problem the example I originally gave here is incorrect. The graph is simple and directed. Key things to remember are that the edges leaving a node all have a number $p$ such that $0 \le p \le 1$, and that the sum of the $p$'s on the edges leaving a single node is one. Also, each edge has a label (a letter is a good example of a label, because then you can think of a path as containing a word, and the probability as the probability of getting that word). The labels are not necessarily unique; in fact a single edge can have more than one identically labelled edge leaving it.

2. example

   Figure 1: Example Problem for Question 2

   

   Group into $k$ "clusters" by choosing three points from the original set and minimizing the distances between each marked point and your chosen point.