Notes on Monte Carlo Simulation in Minitab
Prof. Tom Willemain 2005 Thomas R. Willemain
04/14/09
ENGR 2600 MAU
1
Monte Carlo Simulation
Where possible, we prefer an exact analytical solution using probability theory to estimate the probability

CHAPTER 13
Section 13.1
1. a.
2 ^i is 10 1 - 1 - (x i - 15 ) = = 250 , so s.d. of Yi - Y 5 250
x = 15
and
(x
j
- x)
2
6.32, 8.37, 8.94, 8.37, and 6.32 for i = 1, 2, 3, 4, 5. b. Now
x = 20 and
(x
i
- x ) = 1250 , giving standard deviation

CHAPTER 14
Section 14.1
1. a. We reject Ho if the calculated
2 value is greater than or equal to the tabled value of
2 , k -1 from Table A.7. Since 12.25 .2 , 4 = 9.488 , we would reject Ho . 05
b. c. d.
Since 8.54 is not Since 4.36 is not

CHAPTER 15
Section 15.1
1.
H 0 : = 100 vs. H a : 100 . The test statistic is s + = sum of the ranks associated with the positive values of ( xi - 100) , and we reject Ho at significance level .05 if s + 64 . (from Table A.13, n = 12, with / 2 =

CHAPTER 16
Section 16.1
1. All ten values of the quality statistic are between the two control limits, so no out-of-control signal is generated.
2.
All ten values are between the two control limits. However, it is readily verified that all but one

Introductory Remarks
Introduction
TRW, Adam Petrie
Purpose of course
Cope with uncertainty in analysis and design
Importance of course
Uncertainty is everywhere: In materials, devices, components, systems, measurements, system loads, ambient

Data Plots and Summary Statistics
T. R. Willemain Spring06
1
Agenda
Features of data distributions
Location (mean, median) Spread (standard deviation, IQR) Shape (symmetry, modality, outliers) Association (correlation)
Data displays
Dotplo

Agenda
Definitions: Experiments and random variables Types of RVs: Continuous vs discrete Events and their probabilities Probability distributions: Pdfs and Cdfs Expectations: Mean and variance Using Minitab and Maple
T. R. Willemain MAU Spring

Models of continuous random variables
T. R. Willemain MAU Spring 06
1
Flashback
T. R. Willemain MAU Spring 06
2
Agenda
Frequently used models of continuous random variables Probability plots for matching models to data In-class exercises Mi

Models of discrete random variables
T. R. Willemain MAU Spring 06
1
Agenda
PMF and CDF of discrete RVs Expectations of discrete random variables Frequently used models of discrete random variables In-class exercises Microquiz 05
T. R. Willem

Joint distributions, independence, and applications to reliability of systems
(some bits courtesy of Prof. Pat Sullo)
T. R. Willemain MAU Spring 06 1
Agenda
Joint distributions Independence Application: Reliability of systems In-class exercise

Emily Vilardi
661511452
Number of Hours College Students Sleep Compared to High-School Students
*I spoke with Professor Le Coz and he gave me permission to use a sample of 50 people, and
also allowing that my name, RIN, and title arent on the same line be

CHAPTER 12
Section 12.1
1. a. Stem and Leaf display of temp: 17 0 17 23 17 445 17 67 17 18 0000011 18 2222 18 445 18 6 18 8
stem = tens leaf = ones
180 appears to be a typical value for this data. The distribution is reasonably symmetric in appeara

CHAPTER 11
Section 11.1
1. a.
30.6 59.2 7.65 = 7.65 , MSE = = 4.93 , f A = = 1.55 . Since 1.55 is 4 12 4.93 not F. 05, 4 ,12 = 3.26 , don't reject HoA . There is no difference in true average tire MSA =
lifetime due to different makes of cars.
b.

Functions of random variables, including statistics
Prof. Tom Willemain
T. R. Willemain MAU Spring06
1
Agenda
Functions of RVs
linear/nonlinear functions univariate/multivariate functions independent/dependent RVs Ex: Propagation of error
R

ENGR 2600 Modeling and Analysis of Uncertainty Spring 2006 Project #1: Analysis of observational study using Minitab 14 Student Edition Due: At the start of class 03. Work alone on this project. (In later projects, you will work in teams, but now you

Your RIN Number: _ TA: Adam Petrie
MAU Spring 2006 Exam 1 Section 5 (M/R 8:30-9:50 am)
Academic integrity
Work entirely alone. You cannot share notes, books, calculators, etc. with anybody. Feel free use the textbook and any other written materi

Nicholas Richardson MAU Sec. 3 Project 1
This dataset reflects a set of observations of the sun. The number of sunspots seen each day was recorded over a period of one hundred days. The mean number of sunspots for each day was calculated to be 46.93

Chapter 1: Overview and Descriptive Statistics
CHAPTER 1
Section 1.1
1. a. b. c. d. Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post Capital One, Campbell Soup, Merrill Lynch, Pulitzer Bill Jasper, Kay Reinke, Helen Ford, Dav

CHAPTER 2
Section 2.1
1.
a. S = { 1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3124, 3142, 4123, 4132, 3214, 3241, 4213, 4231 } Event A contains the outcomes where 1 is first in the list: A = { 1324, 1342, 1423, 1432 } Event B contains the outcome

CHAPTER 3
Section 3.1
1. S: X: FFF 0 SFF 1 FSF 1 FFS 1 FSS 2 SFS 2 SSF 2 SSS 3
2.
X = 1 if a randomly selected book is non-fiction and X = 0 otherwise X = 1 if a randomly selected executive is a female and X = 0 otherwise X = 1 if a randomly select

CHAPTER 5
Section 5.1
1. a. b. c. P(X = 1, Y = 1) = p(1,1) = .20 P(X 1 and Y 1) = p(0,0) + p(0,1) + p(1,0) + p(1,1) = .42 At least one hose is in use at both islands. P(X 0 and Y 0) = p(1,1) + p(1,2) + p(2,1) + p(2,2) = .70 By summing row probabi

CHAPTER 6
Section 6.1
1. a. We use the sample mean,
x to estimate the population mean .
^ =x=
b.
xi 219.80 = = 8.1407 n 27
We use the sample median, ascending order).
~ = 7.7 (the middle observation when arranged in x
1860.94 - ( 219.8) 27 s =

CHAPTER 7
Section 7.1
1. a.
z 2 = 2.81 implies that 2 = 1 - (2.81) = .0025 , so = .005 and the confidence
level is 100 1 -
(
)% = 99.5% .
b. c.
z 2 = 1.44 for = 2[1 - (1.44)] = .15 , and 100(1 - )% = 85% .
99.7% implies that
= .003 , 2

CHAPTER 8
Section 8.1
1. a. b. c. d. Yes. It is an assertion about the value of a parameter. No. The sample median
~ X is not a parameter.
No. The sample standard deviation s is not a parameter. Yes. The assertion is that the standard deviation of

CHAPTER 9
Section 9.1
1. a.
E (X - Y ) = E( X ) - E (Y ) = 4.1 - 4.5 = -.4 , irrespective of sample sizes.
V ( X - Y ) = V (X ) + V (Y ) =
of
2 12 2 (1 .8) (2.0) = .0724 , and the s.d. + = + m n 100 100 2 2
b.
X - Y = .0724 = .2691 .
c.
A norm