PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
Homework C
1.
Let X = the number of sampled contracts with cost overruns, so X ~ Bin(20, .2).
20
= =
a. P ( X 4) (.2) 4 (.8)16 = .2182
4
b.
=
=
P( X < 3) P( X= 0,1, 2)
20
2
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
REVIEW SHEET FOR EXAM #1
MONDAY, APRIL 15
TOPICS
WHAT TO BRING



population v. sample, types of
sampling, sampling variation
observational study v. experiment
observational
Probability and Statistics for Scientists and Engineers
STAT 321

Winter 2008
Winter, 2008
Tuesday, Jan. 15
Stat 321 – Lecture 5
Probability Rules (2.2)
Special case: In situations where the outcomes of an experiment are equally likely to occur (e.g.,
tossing a fair coin), the exact probability of an outcome is 1/N, where N is the
Probability and Statistics for Scientists and Engineers
STAT 321

Winter 2008
Stat 321  HW 1 Due beginning of class, Tuesday, Jan. 15 1) This activity asks you to consider the value of statistics ratings that you and your classmates gave to Statistics in the Stat 321 Initial survey (1=completely useless to 9=extremely importa
Probability and Statistics for Scientists and Engineers
STAT 321

Winter 2008
Stat 321  HW 1 Solutions 1) This activity asks you to consider the value of statistics ratings that you and your classmates gave to Statistics in the Stat 321 Initial survey (1=completely useless to 9=extremely important). The responses of the first
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2014
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2014
EXAM #2, VERSION #1
You will need to follow along with your exam.
1.
Draw a tree diagram. Let A = good = inside spec limits, Ac = bad = outside spec limits, R = redflagged, an
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
ASSIGNMENT FOR WEEK #5
Reading: This week, we begin Chapter 4 (were skipping Chapter 3, and well come back to
Chapter 2 later). Read Sections 4.14.4, which discuss six importa
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
ASSIGNMENT FOR WEEK #8
Reading: First, return to Section 2.5, and focus on the subsection The Mean and Variance of a
Sample Mean (pp. 123124).
Next, read Section 4.2 starting
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2014
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2014
EXAM #1, VERSION #2
You will need to follow along with your exam.
1.
a.
b.
The observational units are silicon pillars (n = 50).
The distribution of heights of these 50 silicon
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2014
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2014
EXAM #2, VERSION #3
You will need to follow along with your exam.
1.
Let F = fraudulent tax return and R = redflagged return (so Rc = greenflagged). Construct a tree diagram:
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2014
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2014
EXAM #3, VERSION #2
You will need to follow along with your exam.
1.
a.
b.
c.
d.
Since the points in the normal probability plot lie close to the 45 line, the sample percentile
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2014
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2014
EXAM #1, VERSION #1
You will need to follow along with your exam.
1.
a.
b.
The observational units are silicon pillars (n = 50).
The distribution of heights of these 50 silicon
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2014
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2014
EXAM #2, VERSION #2
You will need to follow along with your exam.
1.
Draw a tree diagram. Let A = good = inside spec limits, Ac = bad = outside spec limits, R = redflagged, an
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2014
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2014
EXAM #3, VERSION #1
You will need to follow along with your exam.
1.
a.
b.
c.
d.
Since the points in the normal probability plot lie close to the 45 line, the sample percentile
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
ASSIGNMENT FOR WEEK #1
Reading: Chapter 1. This week, you will read a lot of material that we wont cover in class (other
than me answering questions), but you are still respons
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
ASSIGNMENT FOR WEEK #7
Reading: First, read all of Section 2.5. This section reviews rescaling properties then discusses
linear combinations of independent random variables. W
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
Homework F
1.
Statement (ii) is the best answer: The variance of an estimator measures how close repeated values of the
estimator are to each other. This is the issue of precis
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
REVIEW SHEET FOR EXAM #2
MONDAY, APRIL 29
TOPICS
WHAT TO BRING
Conditional probability & independence
 definition of conditional probability
 testing for independence
 tree
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
REVIEW SHEET FOR FINAL EXAM
SUNDAY, JUNE 9, 2:10PM5:00PM, IN ROOM 14249
TOPICS
Jointly discrete random variables
 joint probability mass function
 how to calculate marginal
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
REVIEW SHEET FOR EXAM #3
MONDAY, MAY 13
TOPICS
I will provide the standard normal cdf
table, aka (z), from the textbook.
Discrete probability models

Binomial & Negative Binom
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
Homework E
1.
Let X1, , X12 represent the weights of the 12 boxes, which we can treat as i.i.d. with n = 12
(obviously), X = 12.02 oz, and X = 0.03 oz.
a. Let S12 = X 1 + + X 1
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
Homework B
1.
The tree diagram below shows the possibilities in this scenario (D = deploy).
0.99
D1
0.98
D2
0.01
0.02
2.
a. Using the tree diagram, P(D1 D2) = 0.99 + (0.01)(0.9
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
Homework D
1.
a.
By linearity of expectation, R = R1 + R2 = 50 + 100 = 150.
b.
Since R1 and R2 are independent, we have
2
2
2
R =+ = 52 + 102 125 R = 125 = 11.18
R1
=
R2
a.
B
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
ASSIGNMENT FOR WEEK #9
Reading: First, skim Section 4.9. The concepts are more important than the mathematics in this
section. The author talks about the MSE of an estimator, w
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
Homework A
1.
a.
b.
c.
False. As indicated in parts b and c, whether or not we conclude that the new process is better
(meaning the true defect rate for the process is less tha
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Spring 2013
STAT 321: PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
SPRING, 2013
ASSIGNMENT FOR WEEK #3
Reading: Section 2.3. Theres a lot of material in this section, and we will cover some of it
Monday of week 4. But you should read the entire section now
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Fall 2009
Investigation 9: More Battery Lifetimes
Please work with one or two other people on this, handing in one report with all
names. You will submit the report via PolyLearn according to the due date listed on
the Syllabus.
Suppose that the lifetime of a batte
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Fall 2009
Example: German Tank Problem
During World War II, Allied Intelligence (the spies) gave reports on the production of tanks and
other war materials that varied widely and were somewhat contradictory. In 1943 Allied
statisticians (the geeks) trying to improv
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Fall 2009
Due:
Investigation 5: Ice Cream Prices
Please work with one or two other people on this, handing in one report with all
names. You will submit the report via PolyLearn according to the due date listed on
the Syllabus. Integrate appropriate computer output
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Fall 2009
a) Work with a partner (who may or may not be a student in this class) to look through
the American Film Institutes Top 100 list of American films
(http:/www.afi.com/100years/movies10.aspx). Keep track of which movies you have
seen and which your partner
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Fall 2009
Investigation 7: Heart Transplant Mortality
Please work with one or two other people on this, handing in one report with all names. You
will submit the report via PolyLearn according to the due date listed on the Syllabus.
In September of 2000, heart tran
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Fall 2009
Investigation 8: Sampling without Replacement
Please work with one or two other people on this, handing in one report with all
names. You will submit the report via PolyLearn according to the due date listed on
the Syllabus.
Suppose that in a population o
PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS
STAT 321

Fall 2009
Investigation 1: Reducing Back Pain
A study published in the journal Neurology examined whether the drug botulinum toxin A is
helpful for reducing pain among patients who suffer from chronic low back pain. Thirtyone
subjects participated in the study. Th