TASK: Use a transition model to simulate how 800 students shift between three dormitories.
COMMENT: 800 students are assigned to the Able, Babel, and Cable dorms. Every month, they are allowed to change dorms if they want.
The registrar knows the probability that a student living in a dorm will choose to move after a month to Able (A), Babel (B), or Cable (C):
This Month
A B C
-----------------
Next A | 0.90 0.02 0.04
Month B | 0.05 0.68 0.40
C | 0.05 0.30 0.56
For instance, a student living in Cable dorm has an 0.04 probability of
moving to Abel, a 0.40 probablity of moving to Babel, and a 0.56 probablity
of staying in Cable.
The university initially assigns 0 students to Able, 300 to Babel, and 500 to Cable. Simulate the student population for 20 consecutive months.
INSTRUCTIONS:
m = number of months
P = m x m matrix of probabilities
A, B, C = zero vectors of 1 row and m columns each.
loop i from 1 to m
if i is 1,
initialize A(1), B(1), C(1)
else
A(i) = P(1,1) * A(i-1) + P(1,2) * B(i-1) + P(1,3) * C(i-1)
B(i) = ?
C(i) = ?
end
end
plot ( 1:m, A, 1:m, B, 1:m, C )
CHECK:
You might get something like this. I used the legend('A','B','C') command
to connect the line colors to A, B, and C:
SUBMIT: Your script file should be named "hw054.m", and begin with:
% hw054.m
% YOUR NAME
% This script (describe what it does)