Duty Migration Table

Question 1
Q1a) Write down a “duty migration table” containing the probabilities listed above.
Royal Battlement Peace
Royal family 0.7 0.3 0
Battlement 0.4 0 0.6
Peace 0.1 0.4 0.5
Q1b) Peter is a guard currently assigned to peace keeping. However, Peter has a
fear of heights and thus does not enjoy patrolling the battlements. What is the
probability that he will NOT have to patrol the battlements at all within the following
2 weeks?
0.1 R
1/3 0.9 NR
1/3 0.4 B
1/3 0.6 NR
0.5 P
0.5
NP
Note;
R = royal family
NR = not reassigned to royal family
B = Battlement
NB = not reassigned to battlement
P = Peace
NP = not reassigned to peace

P(Not reassigned to patrol battlement) = 1/3*0.6 = 0.2
Q1c) Gambit is another guard, currently assigned to protect the royal family. As an
avid gambler, Gambit has made a bet with some of the other guards. He has made
a bet based on where he will be assigned in 2 weeks’ time, with the following
payoffs:
What is the expected payoff for Gambit, given the information above?
Duty Royal Battlement Peace
Bet $5 $2 $1
Probability Royal
family
0.7 0.3 0
Expected payoff = ∑ piXi
= 0.7 *$5 + 0.3*$2 + 0*$1 = $4.10

Question 2
Q2a) Make an appropriate graph of the pairs of daily returns.
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
Return A
Return B
Q2b) State the Pearson’s correlation coefficient for these daily returns. You do not
need to show any working for this part.
Data calculated from excel for Pearson’s correlation coefficient
Return
A
Retur
n B
Retur
n A 1
Retur
n B
0.4519
17 1
Q2c) Explain what your result in part b) means with reference to your graph in part
a).
The positive coefficient of 0.45 (2 decimal points) indicates that there is a direct connection between
the Return A and Return B, therefore, the more the shares are return back to bank A, the more the
shares too will also be returned back to bank B.
Q2d) Suppose you wanted to simulate more data points to help predict future
returns. First describe what features (in particular, dependencies) of the current
data you would try to preserve. What process would you choose to simulate your
data? Explain how you chosen method would preserve your chosen features.
The features of the current data to be preserve include the dates