HAND IN INSTRUCTIONS: Due: 11:59:59 Wed 7-Dec-2005 Email solution to: barak.pearlmutter+cs401 @ g m a i l . c o m (The suffix allows me to ensure that no messages are lost to spam filters.) Please use a plain ASCII message that includes the labellings of the strings, along with whatever other information (in the form of English text) you wish to impart. Meaning a description of how you solved the problems, any interesting gotchas you encountered and how you overcame them, etc. Any code you wrote should be included as an attachment. There are two problems. Outline first: Problem 1a: label the below dataset as to whether strings come from HMM I vs HMM II. Problem 1b: the same, but with a biased prior (more from HMM I than HMM II) Problem 2: the same, but with a dataset generated by three HMMs, where HMM III is unknown. The below code uses the functions defined in hw3.el, which is written in Emacs Lisp (!) You don't need to understand that code, but you will probably want to extract the parameters (pi, A, B) of Machine I and Machine II from it. You may also find the "HMM Cheat Sheet", pointed to from the class main web page, helpful. Now on to the details, and the data! ---------------------------------------------------------------- Problem 1 First, some sample data for your convenience, eg for debugging and testing. Sample strings generated by Machine I: (print (bunch-o-strings lambda1 100 50)) (0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0) (0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0) (1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1) (0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1) (0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1) (0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0) (0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0) (0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0) (0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1) (0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1) (0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0) (0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0) (0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0) (0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0) (0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0) (0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0) (0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0) (1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1) (0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1) (0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0) (0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1) (0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 1) (0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1) (0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0) (0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0) (0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1) (0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0) (0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 1) (0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1) (0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0) (0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1) (0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 1) (0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1) (0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1) (0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0) (0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0) (0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0) (0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 0 0 0) (0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1) (0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1) (0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1) (0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1) (0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1) (0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0) (0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1) (0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1) (0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1) (0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0) (0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0) (0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0) (0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1) (0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0) (0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1) (0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0) (1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1) (1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0) (0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1) (0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1) (0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0) (0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0) (1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0) (0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1) (0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1) (0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0) (0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 1 1 0) (0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1) (0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0) (0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1) (0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1) (0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1) (1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0) (0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0) (1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1) (0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1) (0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1) (0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1) (0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1) (0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0) (0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1) (0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1) (0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0) (0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0) (0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0) (0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0) (0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0) Sample strings generated by Machine II: (print (bunch-o-strings lambda2 100 50)) (0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0) (0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 0 1 0) (0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1) (0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0) (1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1) (0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1) (0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1) (0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1) (0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 1 1) (1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1) (0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0) (0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0) (0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0) (0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1) (0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1) (0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 1 0) (1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1) (0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0) (0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1) (0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1) (0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0) (0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1) (0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1) (1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1) (0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1) (0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1) (1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0) (0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0) (0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1) (0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0) (0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0) (0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0) (0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 0) (0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1) (1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0) (0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0) (0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1) (0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1) (0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0) (0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0) (0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0) (1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0) (0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0) (1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0) (0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0) (0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 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Dataset of outputs (strings) of two known HMMs, equal priors. P(Machine I) = 0.5 P(Machine II) = 0.5 Problem 1a: assign each string below to its more likely producer. This should be in the form of a list like this (I II II I ...) meaning that the first string was produced by Machine I, the second by Machine II, the third by Machine II, the fourth by Machine I, etc. Test set of strings Generated by Machine I and Machine II, mixed together: Here is the code that generated this data: (setq test1 (bunch-o-strings lambda1 100 50)) (setq test2 (bunch-o-strings lambda2 100 50)) (setq test1+2 (randomize-order (append test1 test2))) (print test1+2) (1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1) (1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 1) (0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1) (0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1) (1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0) (0 0 0 1 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0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1) (0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1) (0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1) (0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1) (0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0) (0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0) (1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 0) (0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 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0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0) (1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1) (0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0) (0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1) (1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0) (0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1) (0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0) (0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0) (0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1) (0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0) (0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0) (0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0) (0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0) (0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1) (1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1) (0 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1) (0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1) (0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1) (1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1) (0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0) (0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1) (0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0) (0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1) (0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1) (0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0) (0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0) (0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0) (1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0) (1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1) (1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1) (0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1) (1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1) (0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1) (0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0) (0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1) (0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0) (0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0) (0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1) (1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1) (0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1) (0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0) (0 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0) (0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1) Problem 1b: same machines, but a different dataset, with a biased prior: P(Machine I) = 0.95 P(Machine II) = 0.05 Here is the code that generated this data: (setq test1 (bunch-o-strings lambda1 95 50)) (setq test2 (bunch-o-strings lambda2 5 50)) (setq test1+2 (randomize-order (append test1 test2))) (print test1+2) (0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0) (0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0) (1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1) (0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1) (0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1) (0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1) (0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0) (0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 0 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1) (0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 0) (0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 0) (0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0) (0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 0) (0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 1) (0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0) (0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1) (0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1) (0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1) (0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1) (0 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0) (0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1) (0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1) (0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1) (0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0) (0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1) (0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0) (0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0) (0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1) (0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 1 0 1) (0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1) (0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 0 1) (0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1) (0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 1 1) (0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1) (0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0) (0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0) (0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1) (0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1) (0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1) (0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1) (0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0) (0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1) (0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1) (0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1) (0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1) (0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0) (0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1) (1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0) (0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0) (0 0 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1) (0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0) (0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 1) (0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1) (0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1) (0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0) (0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0) (0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1) (1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0) (0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0) (0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0) (0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0) (0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1) (0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1) (0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0) (1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1) (0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1) (0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0) (0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1) (0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1) (0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0) (0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1) (0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1) (0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1) (0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 0) (0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1) (1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0) (0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0) (0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0) (0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0) Problem 2: larger dataset, from three models, first two known, equal priors: P(Machine I) = 1/3 P(Machine II) = 1/3 P(Machine III) = 1/3 Identify which of the strings below come from Machine I, Machine II, or Mystery Machine III. This should be in the form of a list like this: (I III II I III ...) meaning the first string is from Machine I, the second from Machine III, the third from Machine II, etc. Here is your dataset: a bunch of strings generated by Machine I, Machine II, and Mystery Machine III, all mixed together. (Machine I and Machine II are as above, in Problem 1 and in the hw3.el file.) Here is the code that generated this data: (setq test1 (bunch-o-strings lambda1 75 50)) (setq test2 (bunch-o-strings lambda2 75 50)) (setq test3 (bunch-o-strings lambda3 75 50)) (setq test1+2+3 (randomize-order (append test1 test2 test3))) (print test1+2+3) (0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1 0) (1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1) (1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 0) (1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1) (0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0) (0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1) (1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1) (0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1) (0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0) (0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1) (0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0) (0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1) (0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 0 0) (0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1) (0 0 0 0 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