Dr. Edwin Romeijn
ESI 6321 Applied Probability Methods in Engineering
Prework Problem Set  Solutions
Class of 2009
 1 
ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING
OUTREACH ENGINEERING MANAGEMENT
Class of 2009
PREWORK PROBLEM SET  SOLUTIONS
Exercise 2.1
(a) P(X
≥
5) = P(1,4) + P(2,3) + P(2,4) + P(3,2) + P(3,3) + P(3,4) + P(4,1) + P(4,2) +
P(4,3) + P(4,4) = 10/16.
(b) P(X
≥
5  First is 3) = P(X
≥
5 and First is 3)/P(First is 3) = (3/16)/(1/4)=3/4.
(c) P(X
≥
5  At least 3 in one die) = P(X
≥
5 and At least 3 in one die)/P(At least 3 in
one die) = (5/16)/(7/16)=5/7.
Exercise 2.5
(a) P(Sunny on Wednesday) = P(Sunny on Tuesday and sunny on Wednesday) +
P(Cloudy on Tuesday and sunny on Wednesday) = (0.30)x(0.60) + (0.70)x(0.30) =
0.18 + 0.21 = 0.39.
(b) P(Sunny on Tuesday and Wednesday) = (0.30)x(0.60) = 0.18.
Exercise 2.7
P(Longterm success) = P(Longterm success  Regularseason show) x P(Regular
season show) + P(Longterm success  Middleseason show) x P(Middleseason show)
= (0.10) x (0.60) + (0.05) x (0.40) = 0.08.
Exercise 2.10
Let S1 denote the lamp comes from first shipment, S2 denote the lamp comes from
second shipment, and D denote the lamp is defective. We want to compare P(S1  D)
to P(S2  D). We have P(S1) = 100/150 = 2/3, P(S2) = 50/150 = 1/3, P(D  S1) = 0.04,
and P(D  S2) = 0.06.
First, P(D) = P(D  S1) x P(S1) + P(D  S2) x P(S2) = 7/150.
Therefore, P(S1  D) = P(D  S1) x P(S1)/P(D) = 8/14, and P(S2  D) = P(D  S2) x
P(S2)/P(D) = 6/14. In conclusion, the lamp is more likely to come from the first
shipment.
Exercise 2.15
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View Full DocumentDr. Edwin Romeijn
ESI 6321 Applied Probability Methods in Engineering
Prework Problem Set  Solutions
Class of 2009
 2 
Let X be the number of courses per week.
(a) 0.05 + 0.15 + 0.25 + 0.25 + 0.15 + 0.10 + 0.05 = 1.
(b) P(X=0) = 0.05.
(c) P(X
≥
3) = 0.25 + 0.15 + 0.10 + 0.05 = 0.55.
(d) P(X
≥
1) = 1  P(X = 0) = 1  0.05 = 0.95.
(e) and (f) Let R denote the net revenue. The following table summarizes the available
options. E[R] = $50,500 and
σ
(R) = $22,600. The best option is to add one more
instructor (marginal increase of $800 in net revenues).
R
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 Spring '07
 JosephGeunes
 Normal Distribution, Standard Deviation, Probability theory, Dr. Edwin Romeijn, applied probability methods, prework problem set

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