Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 2
Due: Friday, Feb 26
Question 1. The following data indicate the gain in reading speed (G) versus the number of weeks
in the program (W ) of 10 students in a speed
IEOR 165 Lecture 8
Quality Control
The idea of statistical quality control is that we will periodically take measurements of
the output of some service system or manufacturing process and then use these measurements
to help identify when the process does
IEOR 165 Discussion 3
February 20, 2015
Question 1. Suppose that when a process is in control each item will be defective with
probability .04. Suppose that your three sigma (z1/2 = 3) control chart calls for taking
daily samples of size 500. What is the
IEOR 165 Discussion 6
March 13, 2015
Question 1. A colony of laboratory mice consists of several thousand mice. The average
weight of all the mice is 32 grams with a standard deviation of 4 grams. A laboratory assistant
was asked by a scientist to select
IEOR 165 Lecture 10
Other Null Hypothesis
1 Goodness of Fit Testing
Suppose an item (or person) has one feature. For instance, this feature might be gender (Male
or Female). Suppose there are r dierent possibilities (more formally, the term category is
us
IEOR 165 Discussion 1
January 30, 2015
Question 1. Each of 2 cabinets identical in appearance has 2 drawers. Cabinet A contains
a silver coin in each drawer, and cabinet B contains a silver coin in one of its drawers and a
gold coin in the other. A cabine
IEOR 165 Lecture 16
Regularization
1 Maximum A Posteriori (MAP) Estimation
The MLE framework consisted of formulating an optimization problem in which the objective was the likelihood (as parametrized by the unknown model parameters) of the measured
data,
IEOR 165 Lecture 9
Weighted Control Charts
1 Other Control Charts
1.1
Fraction Defective
Suppose that when the process is in control, the probability that a single item will be
defective is p. Now suppose X1 , X2 , . . . is zero (with probability 1 p) if
IEOR 165 Lecture 5
Two-Sample Location Tests
1 Framework for Two-Sample Location Tests
In many cases, we are interested in deciding if the mean (or median) of one group of random
variables is equal to the mean (or median) of another group of random variab
IEOR 165 Lecture 18
Support Vector Machines
1 Classication
As a motivating example, suppose we have measurements from people of dierent health
markers (e.g., blood pressure, resting heart rate, weight) and would like to predict whether
or not the person s
IEOR 165 Midterm
March 15, 2016
Name:
Overall:
/50
Instructions:
1. Show your intermediate steps.
2. You are allowed a single 8.5x11 inch note sheet.
3. Calculators are allowed.
1
/10
2
/10
3
/10
4
/10
5
/10
1
1. It has been determined that the relation b
IEOR 165 Lecture 11
Semiparametric Models
1
1.1
Kernel Estimators
Convergence Rate
There is one point of caution to note regarding the use of kernel density estimation (and any
other nonparametric density estimators like the histogram). Suppose we have da
IEOR 165 Lecture 8
Regularization
1
Maximum A Posteriori (MAP) Estimation
The MLE framework consisted of formulating an optimization problem in which the objective was
the likelihood (as parametrized by the unknown model parameters) of the measured data,
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 4
Due: Friday, Apr 8
Question 1. In most of Europe and Asia annual automobile insurance premiums are determined
by use of a Bonus Malus (Latin for Good-Bad) system.
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 2
Due: Friday, Feb 26
Question 1. The following data indicate the gain in reading speed (G) versus the number of weeks
in the program (W ) of 10 students in a speed
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 3
Due: Friday, Mar 11
Question 1. Assume we have one observation X drawn from a normal distribution with unknown
mean and known 2 . And itself follows a normal dist
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 1
Due: Friday, Feb 12
Question 1. Let X1 , . . . , Xn be iid from the pdf
f (x) = x1 ,
0 x 1, 0 < <
R1
Find the method of moments estimator of . (hint: E(X) = 0 x1
AliciaAuduong
BioE10:TR1112:30pm
Prof.JohnsonandGSIMahdinia
BioE10:Homework#3
1.(_/4)
Rir2
6Dij
C (r) =
+ Ar + B
@r = L, C(R) = C 0
@r = center, 0, dc
dr = 0, thereforeA = 0
Rir
A
3Dij + r2
R r
0 = 3Di j
i
RiL2
C 0 = 6D j + B
i
RiL2
C 0 + 6D j = B
IEOR 165 Lecture 12
Support Vector Machines
1
1.1
Classification
Motivating Example
As a motivating example, suppose we have measurements from people of different health markers
(e.g., blood pressure, resting heart rate, weight) and would like to predict
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 5
Due: Friday, Apr 22
Question 1. The PCB concentration of a fish caught in Lake Michigan was measured by a technique that is known to result in an error of measure
BioE 10 Homework 1
1. (_ out of 3 points) The first procedure for synthesizing human insulin in a microorganism is described in Human Insulin: Seizing the Golden Plasmid from Science News
in 1978. Briefly, The A chain and B chain of human insulin were
IEOR 165 Lecture 9
Cross-Validation
1
Cross-Validation
Cross-validation is a data-driven approach that is used to choose tuning parameters for regression.
The choice of the is an example of a tuning parameter that needs to be chosen in order to use
Ridge
IEOR 165 Lecture 10
Distribution Estimation
1
Motivating Problem
Consider a situation where we have iid data xi from some unknown distribution. One problem of
interest is estimating the distribution that is generating the data. There are many useful examp
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Practice Questions (2nd Half)
Question 1. Suppose on any given day you are either happy, so-so or sad. Assume that the
chance of being in these three states tomorrow only de
IEOR 165 Lecture 7
Bias-Variance Tradeoff
1
Bias-Variance Tradeoff
Consider the case of parametric regression with R, and suppose we would like to analyze
the error of the estimate in comparison to the true parameter . There are a number of ways
that we c
IEOR 165 Lecture 20
Semiparametric Models
1 Kernel Estimators
1.1
Convergence Rate
There is one point of caution to note regarding the use of kernel density estimation (and any
other nonparametric density estimator like the histogram). Suppose we have dat
IEOR 165 Lecture 17
Cross-Validation
1 Cross-Validation
Cross-validation is a data-driven approach that is used to choose tuning parameters for
regression. The choice of bandwidth h is an example of a tuning parameter that needs to be
chosen in order to u
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 5
Due: Friday, Apr 22
Question 1. The PCB concentration of a fish caught in Lake Michigan was measured by a technique that is known to result in an error of measure
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 3
Due: Friday, Mar 11
Question 1. Assume we have one observation X drawn from a normal distribution with unknown
mean and known 2 . And itself follows a normal dist
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 6
Due: Friday, May 6
Question 1. Suppose we have conducted 6 null hypothesis tests, with p-values as
Test #
p-value
1
2
3
4
5
6
0.006
0.035
0.002
0.041
0.023
0.078
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 1
Due: Friday, Feb 12
Question 1. Let X1 , . . . , Xn be iid from the pdf
f (x) = x1 ,
0 x 1, 0 < <
R1
Find the method of moments estimator of . (hint: E(X) = 0 x1
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2016)
Homework 4
Due: Friday, Apr 8
Question 1. In most of Europe and Asia annual automobile insurance premiums are determined
by use of a Bonus Malus (Latin for Good-Bad) system.