Question:

Journal 12: Some say we accomplished 8 years of digital evolution in 8 months during the pandemic... agree? more class materials.. Journal 13: The Waterfall Methodology for IT Projects is one of the oldest software development methods (35+ years). It has a success rate of only 10%. One of the biggest problems with the Waterfall Methodology is that assumes users of the software can specify all business requirements in advance. What step in the SDCL are VALID business requirements gathered? Another issue with Waterfall is that it assumes business requirements don't change over time. If you find yourself on a software development project, What are some Agile Methodologies you could consider to help increase the success rate? And what are the features of those Agile Methodologies? Journal 14: What are your thoughts regarding information and cyber security, the world we live in today and IoT regarding the above Current Event? Current Events: Gasoline and oil prices rise as a U.S. pipeline remains shut after cyber attack. Journal 15: The Colonial Pipeline is the largest pipeline system for refined oil products in the United States? Well, last Friday this jewel in the crown of our oil and gas industry had to be shut down, after a ransomware attack by a gang of criminal hackers called DarkSide occurred the day before. Naturally we've all heard in the news about the immediate consequences of Americans who live on the East Coast: Gas shortages intensifying in the Southeast with, for example, 28 percent of North Carolina stations now dry. We've all heard on the same news about ransomware, and how the Biden administration is prepping to ramp up U.S. cyber defenses. But, have you heard anywhere why this ransomware attack was made possible? Because without tackling the problem at the core, ransomware and other cyberattacks will continue to flourish. Journal: What are some topics from class that come to mind with this current event news story?

For each of the following transition matrices, determine whether the Markov chain with that transition matrix is regular: (1) Is the Markov chain whose transition matrix whose transition matrix is 0 0.5 0.5 0.5 0 0.5 0 0 regular? (Yes or No) (2) Is the Markov chain whose transition matrix whose transition matrix is 0 1 0 0.3 0 0.7 0 0 regular? (Yes or No) (3) Is the Markov chain whose transition matrix whose transition matrix is 0 1 0 0.6 0 0.4 1 0 0 regular? (Yes or No) (4) Is the Markov chain whose transition matrix whose transition matrix is 0 1 0 0 0.6 0 0.4 regular? (Yes or No) (5) Is the Markov chain whose transition matrix whose transition matrix is 0 1 0 0.3 0.2 0.5 0 1 0Given a Markov chain with transition matrix P and stationary distribution , the time reversal is a Markov chain with transition matrix P defined by P for all i. j. (a) Show that a Markov chain with transition matrix P is reversible if and only if P = P. (b) Show that the time reversal Markov chain has the same stationary distribu- tion as the original chain.1. Consider the Markov chain with three states, S=(1,2,3), that has the following transition matrix: 0.7 0.2 0.1 P = 0.1 0.5 0.4 0.3 0.3 0.4 with initial distribution 7 = (0.6;0.4; 0.0). 1) Plot state transition diagram of the Markov Chain; 2) Find the Markov transition matrix after 2 steps; 3) Find the Markov Chain distribution after two steps; 4) Find the Markov chain realization: P($1=E2, 52= El, (4= E3, $7=E1). 5) Find the stationary distribution of the Markov Chain - (co)1. Consider the Markov chain with three states, S={1,2,3), that has the following transition matrix: 0.6 0.3 0.1 P = 0.5 0.0 0.5 0.2 0.4 0.4 with initial distribution 7 = (0.7;0.2; 0.1). 1) Plot state transition diagram of the Markov Chain; 2) Find the Markov transition matrix after 2 steps; 3) Find the Markov Chain distribution after two steps; 4) Find the Markov chain realization: P(1=E3 , (3=El , 84=E2, 87=ED). 5) Find the stationary distribution of the Markov Chain - (co)