PROBLEM SET: DECISION TREE
SOLUTIONS
PROBLEM D.1
Solution: The payoff function is given below:
Decision
BUY
NOT BUY
BANQUET (State)
CANCELLED
NOT CANCELLED
-2
198
0
-100
a)! The worst payoff associate
PROBLEM SET: DECISION TREE
QUESTIONS
PROBLEM D.1
Question: The following question is adapted from an argument of the seventeenth century French mathematician
and philosopher Blaise Pascal.
Suppose tha
A Review:
In high school, students were taught how to graph linear equalities such as y = 3x + 4
(which graph as lines) and linear inequalities y 3x + 4 (which graph as shaded regions).
Y
Y <= 3X + 4
Springfield Police Solution
a. See below for model.
b. Model 1 is infeasible. There is no way to get the coverage required with 30
officers. Recommendations can include hiring more officers or
PROBLEM SET: PROBABILITY
SOLUTIONS
PROBLEM P.1
Solution:
a)! P(A B) =
P(A ! B) 0.40
=
= 0.6667
P(B)
0.60
b)! P(B A) =
P(A ! B) 0.40
=
= 0.80
P(A)
0.50
c)! Not independent since P(A|B) " P(A).
(The pro
LP Practice Problem Springfield Police
The Springfield City Police Department employs 30 police officers. Each officer works 5
consecutive days per week. The crime rate fluctuates with the day of the
PROBLEM SET: PROBABILITY
QUESTIONS
PROBLEM P.1
Question: For two events A and B, P(A) = 0.5, P(B) = 0.60 and P(A!B)=0.40.
a)! Find P(A|B).
b)! Find P(B|A)
c)! Are A and B independent?
PROBLEM P.2
Ques
PROBLEM SET: RANDOM VARIABLES
QUESTIONS
PROBLEM R.1
Question: Shown below is the probability distribution for the random variable X:
x
3
6
9
Total
a)! Compute the expected value of X.
b)! Compute the