IE 4521 Statistics, Quality, and Reliability
University of Minnesota, Fall 2011
Instructor:
Dr. Kevin Leder
Oce: ME 130A
Phone: (612) 624-7965
Email: [email protected]
Oce Hours:
Monday 10:00 AM11:00 AM
Wednesday 2:00 PM3:00 PM
or by appointment
Requ
More Practice Problems
IE 4521 Fall 2011
1
Midterm 1
1.6.4
Let A1 , A2 and A3 be the event that the observed bird is of species 1, 2 and 3, respectively. Let B be the
event that a tagged bird is observed. Then P (B |A1 ) = 0.1, P (B |A2 ) = 0.15, P (B |A
IE 4521 Midterm #1
Prof. John Gunnar Carlsson
March 2, 2010
This exam has 9 pages (including the normal distribution table) and a total of 8 problems.
Make sure that all pages are present. To obtain credit for a problem, you must show all your work. if yo
IE-4521 Practice Problems for Midterm 1
1. From a group of 3 freshmen, 4 sophomores, 4 juniors, and 3 seniors a committee of size 4 is
randomly selected. Find the probability that the committee will consist of
(a) 1 from each class
(b) 2 seniors and 2 fre
IE 4521 Midterm Exam 1
Write clearly, and circle your nal answer.
On problems 1-5 you must show your work to receive credit.
Name
Problem
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
6
1
/20
/20
/20
/20
/20
/20
/120
Problem 1
Suppose that you a
IE 4521 Midterm #2
Prof. John Gunnar Carlsson
April 12, 2011
Before you begin: This exam has 10 pages (including the quantile tables for the t- and
F -distributions)
and a
total of 6 problems. Make sure that all pages are present. To obtain credit for a p
IE 4521 Midterm Exam 2
Fall 2011
Write clearly, and circle your nal answer.
On problems 1-5 you must show your work to receive credit.
Name
Problem
Problem
Problem
Problem
Problem
Problem
Bonus
Total
1
2
3
4
5
6
1
/15
/20
/25
/20
/20
/20
/5
/120
Problem 1
PRACTICE PROBLEMS
1. Midterm 1
(1) Problems 1.6.4,1.6.5 from book.
(2) Problems 2,4,5 Fall 2011 Midterm1
(3) One thousand independent die rolls are made. Approximate the probability that
the number 6 will appear between 150 and 600 times.
(4) If X1 , . .
IE 4521 Midterm #1
Prof. John Gunnar Carlsson
March 2, 2010
This exam has 9 pages (including the normal distribution table) and a total of 8 problems.
Make sure that all pages are present. To obtain credit for a problem, you must show all your work. if yo
IE 4521 Midterm #1
2
Prof. John Gunnar Carlsson
April 12, 2011
Before you begin: This exam has 11 pages (including the quantile tables for the t- and
F -distributions)
and a
total of 6 problems. Make sure that all pages are present. To obtain credit for a
Problem 1
70 + 16
= 0.86
100
70 + 9
(b) P ( B) =
= 0.79
100
(a) P ( A) =
(c) P ( A / B ) =
P ( A B ) 70 /100
=
= 0.886
P( B)
79 /100
(d) P ( B / A) =
P ( B A) 70 /100
=
= 0.814
P( A)
86 /100
Problem 2
This circuit includes three parts, the left part, the
IE 4521 Homework 1
1.2.10
(a) See Figure 1.24
P(Type I battery lasts longest)=P(II,III,I)+P(III,II,I)=0.39+0.03=0.42
(b) P(Type I battery lasts shortest)=P(I,II,III)+P(I,III,II)=0.11+0.07=0.18
(c) P(Type I battery does not last longest)=1-P(Type I battery
4.2.1
0
0
E ( X ) =f ( x) dx = e x dx
x
x
= x d (e
x
) = x e
0
= 0 + (
1
| + e x dx
x
0
0
e x ) |0 = (
1
1
1
e x ) |0 = 0 ( ) =
2
E ( X ) = f ( x) dx = e x dx
x
x
2
2
0
0
= x 2 d (e x ) =x 2 e x | + e x d ( x 2 )
0
0
0
=0 + 2 xe x dx =
0
2
x e
0
x
5.4.1
(a) E ( X ) e= 10.23
= 1.2+ (1.5 /2)
2
(b) Var ( X )= e(21.2) +1.5 (e1.5 1 )= 887.69
2
2
(c) Since z0.25 = 0.6745 , the upper quartile is e1.2+ (1.50.6745) = 9.13
(d) the lower quartile is e1.2+ (1.5( 0.6745) = 1.21
(e) the interquartile range is 9.
Practice Final Exam
May 4, 2010
1
New Material
1.1
ANOVA
1. A purication process for a chemical involves passing it, in solution, through a resin on which impurities are
adsorbed. A chemical engineer is testing the eciency of 3 dierent resins in collectin
1. Problem 7.2.8 in the text.
2. Suppose that a
6-sided die is rolled n times, showing values X1 , . . . , Xn . Make
1 on the die, and write the standard error of this estimate.
a point estimate of the
probability of rolling a
3. Determine the maximum lik
IE 4521 Practice Midterm Problems
John Gunnar Carlsson
October 22, 2009
1
Probability problems
1.1
Dice
Suppose we roll a pair of dice:
1. What is the probability that the second die lands on a higher value than the rst die?
2. What is the probability tha
IE 4521 Final exam
Prof. John Gunnar Carlsson
December 15, 2009
Before you begin: This exam has 11 numbered pages and a total of 8 problems. Make sure that all pages are
present.
To obtain credit for a problem, you must show all your work.
if you use a fo
IE 4521 Final exam
Prof. John Gunnar Carlsson
December 15, 2009
Before you begin: This exam has 11 numbered pages and a total of 8 problems. Make sure that all pages are
present.
To obtain credit for a problem, you must show all your work.
if you use a fo
3 Building Blocks of Probability
1. Sample space: Denoted by S . Collection of all possible
outcomes of random experiment, and each outcome
corresponds to one and only one element in the sample space
(i.e., sample point).
2. Event: Any subset of S.
3. Pro
IE 4521: Statistics, Quality, and Reliability
Lecture 5: Reliability Theory, Midterm Exam Review
John Gunnar Carlsson
March 4, 2013
John Gunnar Carlsson
IE 4521: Statistics, Quality, and Reliability
March 4, 2013
1 / 14
Administrivia
Midterm exam next wee
IE 4521 Midterm #1
Prof. J. G. Carlsson
February 22, 2011
Before you begin: This exam has 13 pages (including the normal distribution table) and a total of 6 problems.
Make sure that all pages are present. To obtain credit for a problem, you must show all
Solution 7
IE 4521 Fall 2011
7.6.5
1
p.
1
So the method of moments gives p = x . The
likelyhood function is L(x1 , . . . , xn , p) = pn (1 p)x1 +xn n . The log-likelyhood function is L = n log p + (x1 +
+ xn n) log 1 p. Taking L = n x1 +xn n = 0, we get
IE 4521 Midterm #2
Prof. John Gunnar Carlsson
April 20, 2010
This exam has 11 numbered pages and a total of 8 problems. Make sure that all pages are
present. To obtain credit for a problem, you must show all your work. if you use a formula to answer a
pro
Solution 6
IE 4521 Fall 2011
7.4.5
(a). A gamma random variable X with parameters k = 5 and has expectation E(X) =
5
5
moment, solving x = , we get = x .
5
.
By the method of
(b). A gamma random variable X with parameters k = 5 and has a probability de