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
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 3
Due: Thursday Mar 16
Question 1. Recall from the previous homework the maximum likelihood estimate derived from
iid data X1 , . . . , Xn with the pdf
f (x) = 2 xe
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 1
Due: Thursday, Feb 9
NOTE: The solutions to this HW will be posted in one week. Please do not write your solutions
in red ink as this HW should be self graded or
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 5
Due: Thursday, May 4
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 measur
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 4
Due: Thursday, April 20
Question 1. A normal population distribution is known to have standard deviation 25. Determine
the p-value of a test of the hypothesis tha
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 2
Due: Thursday, March 2
Question 1. Let X1 , . . . , Xn be iid from the pdf
f (x) = 2 xex ,
0 < x, 0 < <
Find the MLE of .
Solution. The likelihood function is gi
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 3
Due: Thursday Mar 16
Question 1. Recall from the previous homework the maximum likelihood estimate derived from
iid data X1 , . . . , Xn with the pdf
f (x) = 2 xe
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 1
Due: Friday, Feb 9
NOTE: The solutions to this HW will be posted in one week. Please do not write your solutions
in red ink as this HW should be self graded or pe
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 5
Due: Thursday, May 4
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 measur
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,
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 4
Due: Thursday, April 20
Question 1. A normal population distribution is known to have standard deviation 25. Determine
the p-value of a test of the hypothesis tha
Department of Industrial Engineering & Operations Research
IEOR 165 (Spring 2017)
Homework 2
Due: Thursday, March 2
Question 1. Let X1 , . . . , Xn be iid from the pdf
f (x) = 2 xex ,
0 < x, 0 < <
Find the MLE of .
Question 2. Let X1 , . . . , Xn be iid
IEOR 165 Lecture 3
Linear Regression
1
Estimating a Linear Model
Recall that the amount of energy consumed in a building on the i-th day Ei heavily depends on
the outside temperature on the i-th day Ti . Generally, there are two situations. When the outsi
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 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,
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 Midterm
March 15, 2016
Name:
Overall:
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Instructions:
1. Show your intermediate steps.
2. You are allowed a single 8.5x11 inch note sheet.
3. Calculators are allowed.
1
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2
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3
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4
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5
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1
1. It has been determined that the relation b
Forecasting
Mariana Olvera-Cravioto
UC Berkeley
[email protected]
October 4th, 2016
IND ENG 150, Production Systems Analysis
Forecasting
1/4
Background
I
A big-name pharmaceutical company needs to create sales forecasts for
their Product X.
I
Prod
IEOR 165 Lecture 19
Multiple Testing
1
Example: Comparing Restaurant Quality
Consider the following hypothetical situation: There is a chain of fast food restaurants that
is facing decreased customer satisfaction and revenues, and management believes the
IEOR 165 Lecture 22
Weighted Control Charts
1
1.1
Other Control Charts
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
Heteroscedasticity
1
Residuals Plot
Another approach to evaluating the the quality of a linear model is to plot the residuals. That is
we generate a scatter plot of the points (xi , yi yi ). If the variation in the y-direction does not
IEOR 165 Lecture 20
Multiple Comparisons
1
Example: Comparing Service Rates
Consider a situation in which there are four healthcare providers performing triage for an emergency room in a hospital. Triage is the process of evaluating the severity of a pati
IEOR 165 Lecture 21
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