Name: 

Use the following information to answer questions 1-3:
Students at Phoenix High School are given the option to take their math classes in a traditional face-to-face (F2F) setting or on a Computer Self Directed Learning (SDL) version.

Face-to-Face	Self-Directed-Learning

A survey was given at the school and found that initially 39% of students were taking F2F classes and 61% were taking SDL (Computer) classes.

In this example, what is the initial distribution matrix, [D₀], for a Markov chain?

(Using the information above) Approximately how many students will be in each type of class next semester based on the suggested percentages?

(Using the information above) Which Tree Diagram below correctly shows how to find the percentage of students taking each course type in the upcoming semester?

In Tate, Georgia an anonymous political survey was conducted of all 380 citizens. The survey showed that  40% of the population identified themselves as democrats, 45% of the population identified themselves as republicans, and 15% of the population identified themselves as independents.

• Of the population that identified themselves as democrats, 90% suggested they would continue identifying themselves as democrats, but 6% wanted to switch to republican, and 4% wanted to switch to independent  in the upcoming election.
• Of the population that identified themselves as republicans, 82% suggested they would continue identifying themselves as republican, but 10% wanted to switch to democrat, and 8% wanted to switch to independent in the upcoming election.
• Of the population that identified themselves as independents, 95% suggested they would continue identifying themselves as independents, but 3% wanted to switch to democrat, and 2% wanted to switch to republican in the upcoming election.

In this example, what is the initial distribution matrix, [D₀], for a Markov chain?

A large group of people were studied in one town to see which car service they preferred between Ewe-Ber Transport or Swyft Transport
 

Ewe-BER	SWYFT

A survey was given at the school and found that initially 67% of the population preferred  Ewe-BER transport and 33% of the population preferred SWYFT transport.
In this example, what is the transition matrix, [T], for a Markov chain?

The following shows a graph of the probability of a student to be “present” or “absent “ from in a Pre-Calculus class during the flue season.


In this example, what would the transition matrix, [T], be for a Markov chain?

A large sample of customers were given a survey in the U.S. in 2017 about what type of computer and operating system they preferred to use. The following was determined
  

Windows Based PC	Apple Based PC

The study found that initially 86% of the population preferred Windows Based PC’s and 14% of the population preferred Apple Based PC’s.
If the rates remain constant for the next several decades and both types of PC’s are still available what would be the approxiate final distribution percentage of users for each type of PC?

The following shows a graph of the rates at which customers purchasing habits on 2 different battery brands (Durability and Re-energize) based on a study done at an electronics store “Bettter Buys”.  The graph shows the percentage of customers that purchase the same brand again and the percentage that switch brands.


If the inital distribution showed that 68% of the population purchased the Durability brand of batteries  and 32% of the population purchased Re-energize batteries.  If the rates remained consistent what would be the final distributions approach?