Skylos trigurna stous akeraious

H alliws "giati ta polla mathimatika vlaptoun tin psixiki hygeia"...

Mathima: Information Theory
Mathimatikotita: 8/10
Dyskolia: Metria (prin deis tis askiseis)
--------------Kamposi (afou deis tis askiseis)
Kefalaio: Entropy rate of a stochastic process
Askisi: Entropy rate of a dog looking for a bone (!)

A dog walks on the integers(!), possibly reversing direction at each step with probability p=0.1. Let X0=0. The first step is equally likely to be positive or negative. A typical walk might look like this:

(X0,X1, . . .) = (0,-1,-2,-3,-4,-3,-2,-1,0,1, . . .)

(a) Find H(X0,X1, . . ,Xn)
(b) Find the entropy rate of the dog (!)
(c) What is the expected number of steps that the dog takes before reversing direction?

Mporei stin teliki, na min einai poly dyskoli askisi, omws to olo skeptiko nomizw einai teleiws "geia sou"