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 variance of X.
c)! Compute the standard deviation of X.
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 associated with BUY is -2. The worst payoff associated with NOT
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 that Micah is a die-hard fan of the Vancouver Whitecaps, a
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
X
So how does this help us in Commerce 290? Take for ex
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 reducing the
requirements.
c. Model 2 requires 31 o
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 probability of A may depend on whether B takes place or no
PROBLEM SET: RANDOM VARIABLES
SOLUTIONS
PROBLEM R.1
Solution:
a)!
x
3
6
9
Sum
P(x)
0.25
0.50
0.25
1.00
x
3
6
9
Sum
x-E[X]
-3
0
3
x*P(x)
0.75
3.00
2.25
6.00
Thus, E[X] = 6.
b)!
(x-E[X])2
9
0
9
Thus, VAR[X] = 4.5.
c)! Standard deviation of X is the square r
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 week, so the
number of police officers required each da
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
Question: A survey of MBA students obtained the following d