Finite Math 8.1 to 8.3 Review Sheet
Name:
1.A Markov chain has the transition diagram
shown below. Find the transition matrix
for this Markov chain.
4. A Markov chain has the transition matrix
P shown below. The system is initially in
state 1. Find the probability that it is in
state 2 after two transitions.
P=
Answer:
5. A Markov chain has the transition
Answer:
[
]
2.A Markov chain has the transition matrix P
matrix P shown below. Find the
probability that the system makes a
transition from state 1 to state 2 in two
steps.
P=
shown below. If the system is initially in
state 1, find the probability that after one
transition it is in state 3.
Answer:
6. Transition matrices for three Markov
chains are shown below. Which are the
transition matrices of regular Markov
chains?
Answer:
A=
B=
3.Each day a sales representative is either in the
office or out making calls. If she is in the
office one day, then she is in the office
the next day with probability .3, and if
she is out making calls one day then she
is in the office the next day with
probability .4. Formulate a follows: If
she is in the office, then the system is in
state 1 and if she is out making calls,
then the system is in state 2. The system
is observed once each day.
C=
Answer:
7. A regular Markov chain has the
transition matrix P shown below. Find
the first coordinate of the stable vector
for this Markov chain.
P=
Answer:
Answer:
8. Find the long – run batting average of a
softball player who knows that if she
gets a hit, then she gets a hit the next
time with probability .5, but if she makes
an out, then she gets a hit the next time
with probability .3. (Assume each time
up she either gets a hit or makes an out.)
Answer:
1. ANS:
PTS: 1 DIF: E
REF: 8.1
OBJ: 8-1 To set up and interpret the transition
matrix of a Markov chain
2. ANS: .1
PTS: 1 DIF: E
REF: 8.1
OBJ: 8-1 To set up and interpret the transition
matrix of a Markov chain
3. ANS:
PTS: 1 DIF: M
REF: 8.1
OBJ: 8-1 To set up and interpret the transition
matrix of a Markov chain
4. ANS: .48
PTS: 1 DIF: M
REF: 8.2
OBJ: 8-2 To compute new state vectors
5. ANS: .24
PTS: 1 DIF: M
REF: 8.2
OBJ: 8-2 To compute new state vectors
6. ANS: A
PTS: 1 DIF: M
REF: 8.3
OBJ: 8-3 To find regular transition matrices
and stable vectors
7. ANS:
PTS: 1 DIF: H
REF: 8.3
OBJ: 8-3 To find regular transition matrices
and stable vectors
8. ANS: .37
PTS: 1 DIF: M
REF: 8.3
OBJ: 8-3 To find regular transition matrices
and stable vectors