Your task here is to answer the following two questions and you may submit your
ID: 3324818 • Letter: Y
Question
Your task here is to answer the following two questions and you may submit your answer through Blackboard (you can scan or simply take a picture and upload it on Blackboard).
Question Setup:
You are playing a board game that for each turn you will roll a game die and the output will determine where you will go. After you finish one move, you roll the die again and repeat this till the game ends.
There are five(5) places on the board, namely Place A, B, C, D, and E. You start from Place A and you roll the game die.
When you are at Place A, the chances for you, after your rolling, to move to Place B, C, or D are ¼, ¼, and ½, respectively.
Similarly, when you are at Place B, the chances for you to move to Place A, C, or D are ¼, ¼, and 1/4, respectively and there is ¼ chance you will stay at B after your roll.
When you are at Place C, the chances for you to move to Place A, B, D, or E or simply staying at C are equally likely.
When you are at Place D, you will have 1/3 chance to get back to A, 1/3 change to stay at D, and 1/3 change to move to Place E.
When you are at Place E, you will just stay E forever and that is when you win (the game ends).
It does not sound like a really fun game but it has lots of characters of a Markov Chain (if you are interested, you can analyze Monopoly using Markovian process).
Question 1: Write down the transition matrix.
Question 2: What is the probability for you to land on Place C after three moves? (You do not really need to know Markov chains to answer this question.)
Explanation / Answer
1)
2) start is from place A
After 1st move : (0, 1/4, 1/4, 1/2 , 0)
After 2nd move ; (0.28 , 0.11 , 0.11, 0.28, 0.22)
After 3rd move : (- , - ,0.1195,-,-)
A B C D E A 0 1/4 1/4 1/2 0 B 1/4 1/4 1/4 1/4 0 C 1/5 1/5 1/5 1/5 1/5 D 1/3 0 0 1/3 1/3 E 0 0 0 0 1Related Questions
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