1. (10 points) (Without Python) In computer security applications, a honeypot is a trap set on a network to detect and counteract computer hackers. Honeypot data are studied in Kimou et al. (2010) using Markov chains. The authors obtained honeypot data from a central database and observed attacks against four computer ports – 80, 135, 139, and 445 – over 1 year. The ports are the states of a Markov chain along with a state corresponding to no port is attacked. Let (Xn)∞
need help with #1 and #2, but I will post #2 again, thanks for help
. pom s 1 on on n compu er securi y app 1ca ions, a oneypo is a rap se ona network to detect and counteract computer hackers. Honeypot data are studied in Kimou eta1. (2010) using Markov chains. The authors obtained honeypot data from a central databaseand observed attacks against four computer ports — 80, 135, 139, and 445 — over 1 year. Theports are the states of a Markov chain along with a state corresponding to no port is attacked. Let (anfiio be a SDTMC where Xn represents the port attacked with S = {80, 135, 139, 445, No attack}. Weekly data are monitored, and the port most often attacked during the week is recorded. Theestimated Markov transition matrix for weekly attacks is 0 0 0 0 10 8/13 3/13 1/13 1/13F: 1/16 3/16 3/8 1/4 1/80 1/11 4/11 5/11 1/110 1/8 1/2 1/8 1/4 with initial distribution 11 = (0, 0, 0, 0, 1). (a) Which are the least and most likely attacked ports after 2 weeks? (You may need to usea computer for this calculation. Be sure to write down all of your steps and any newmatrices that you compute.) (b) Compute the probability that PU(X100 = j) for all j E S. (You may need to use a computerfor this calculation. Be sure to write down all of your steps and any new matrices thatyou compute.) 2. (30 points) (With Python) In this Python exercise, you will be estimating the probability eachport is attacked after 100 weeks. Be sure to annotate your code with short explanations ofwhat you are doing (worth 10 points). Suppose (as above) that each week the port most often attacked is recorded. The transitionmatrix for weekly attacks is P with initial distribution 1/ (as above).