1: We wish to study graduation rates at a 2 year institution. We will put the st
ID: 2968306 • Letter: 1
Question
1: We wish to study graduation rates at a 2 year institution. We will put the students
in one of 4 categories:
A. First year students.
B. Second year students.
C. Graduates.
D. Students who have dropped out.
If a student enters the first year, then by the end of the year
the probability that the student will move from the rst year to the second is 80%;
the probability that the student will repeat the first year is 10%;
the probability that the student will drop out is 10%; and
the probability that the student will graduate is 0%:
If a student enters the second year, then by the end of the year
the probability that the student will graduate is 80%;
the probability that the student will repeat the second year is 10%;
the probability that the student will drop out is 10%; and
{the probabliity that the student will graduate is 80%:
If a student has dropped out, then
The probability that the student will enter the program a gain is 0%:
Once a student has graduated, then
The probability that they will stay graduated is 100%:
We describe the number of students in each of the categories by a column vector of
length 4 with the rst entry giving the number of students in category A, the second entry
giving the number of students in category B, ... . We watch the progress of a xed group
of students. We do not consider the students coming before or after our group.
1a: What is the matrix which describes the how the students move from one category to
another each year?
1b: At the beginning of the first year there are 100 students, so
(100)
(0)
(0)
(0)
describes the distribution of students among our four categories. What is the distribution after one
year? after two years?
I have a lot of trouble with word problems, I don't exactly know what its asking for .. can some one please answer and then clarify ?
Explanation / Answer
0.8 0.0 0.0 1.0
0.1 0.1 0.0 0.0
0.1 0.1 0.0 0.0
0.0 0.8 1.0 0.0
is the matrix
now
after first year it is (80 10 10 0)
after second year (0 10 10 80)
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