Psychology 449
Fall 2017
"Decision Processes: An Everyday Life Perspective"
Unit A (Basics) Concept List: Lectures 1 2, Discussion 1,
Article 1
Preliminary Version
Note: Concept refers to true concepts, phenomena, processes,
principles, and theories, too.
Stat 401
Fall 2017
Shyamala Nagaraj
Slides #2
1
Topics
Characterizing Distributions: Discrete RVs
Probability Mass Function
Examples
Cumulative Distribution Functions
Means:
Variances
Characterizing Distributions: Continuous RVs
Probability Density Func
STATS 412 EXAM 1 REVIEW WINTER 2017
Note: This review is based on old exam questions, so the questions are representative of the types of
questions you could see. There are no guarantees that the exam looks like the exam review. Make sure
to look at the n
Statistics 412: Homework #3
Due Wednesday, February 1
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made the calculation.
Also be sure to
Statistics 412: Homework #4
Due Wednesday, February 8
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made the calculation.
Also be sure to
Statistics 412: Homework #1
Due Wednesday, January 11
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made the calculation.
Also be sure to
Statistics 412: Homework #5
Due Wednesday, February 22
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made the calculation.
Also be sure t
Stats 250 Fall 2016: Final Exam Review
1. Unusual Average Score or Not? Scores for incoming students on a placement exam are modeled with a normal
distribution having a mean of 100 points and a standard deviation of 10 points. How likely would it be to se
STATS 426
Winter, 2017
Practice Exam #1
Printed Name:
Signature:
UM unique name:
1) Put down your printed name and sign; I will take off 1 pt if they are missing.
2) Show your work and derivations, except for the sub-problems in Problem #1. A correct an
Parameter Estimation
Stats 426 - Point Estimation Introduction &
Approaches
Typical scenarios in practice: We observe data X1 , X2 , . . . ,Xn and
make the assumptions that they are i.i.d. observations from ONE
distribution in order to study them systemat
Stats 426 - Joint Distributions
Chap. 3
In many experiments there are two or more variables of interest.
Examples:
In an agricultural experiment we might measure: yield, rainfall,
temperature,. . .
In a medical study, we measure a patients height, weight,
Expected Value
Stats 426 - Moments
Chap. 4
Suppose X is a discrete random variable with a pmf p. The expected
value of X is given by
X
E (X ) =
xp(x),
x
P
provided that x |x|p(x) < . If this sum is infinite, the expected
value is undefined.
Suppose X is a
Stats 426 - Limit Theorems
We are interested at learning the limiting behavior of the sum (or the
average) of independent r.v. when the number of summands becomes
large.
2
Consider XP
1 , X2 , . . . , Xn are iid with mean and variance . and
1
Xn = n
i Xi
Homework 6 Solutions
Statistics 426
March 7, 2017
1. (6.10)
Let W = (n 1)S 2 / 2 . We know that W follows a chi-square distribution with n 1
degrees of freedom (Theorem B in Section 6.3). Further, we let F2 (s; n 1) denote
the CDF of a 2 -distribution wit
Homework 7 Solutions
Statistics 426
March 10, 2017
1. (8.5)
(a)
E[X] =
2
X
xi P (X = xi ) = 1() + 2(1
) = 2
i=1
=2
So, X
= 5/3
and then plug in the observations of X, we get X
= 2
=1
X
3
(b)
L(|X) = P (X = 1)P (X = 2)2 = (1
)2
(c)
`(|X) = log + 2 log(
Homework 3 Solutions
Statistics 426
January 30, 2017
1. (2.59)
FY (y) = P (Y y) = P (U 2 y) = P ( y y y)
Z y
1 y
1
=
dy = u|y = y
2
y 2
d
1
fY (y) =
y = ,0 < y 1
dy
2 y
2. (2.60)
d 1
Let g(y) = ey . Then g 1 (y) = log y and | dy
g (y)| = y1 .
d 1
1
g (y
Homework 2 Solutions
Statistics 426
February 2, 2017
1. (2.21)
Using Bayes Theorem,
P (X > n + k 1|X > n 1) =
=
P (X > n 1|X > n + k 1)P (X > n + k 1)
P (X > n 1)
P (X > n + k 1)
P (X > n 1)
=
(1 p)n+k1
(1 p)n1
= (1 p)k = p(X > k)
The probability of succe
Homework 5 Solutions
Statistics 426
February 16, 2017
1. (4.74) Let the first generation begin with 1 subject. For the second generation, the
total number of offspring X will have
V ar(X) = 2
E[X] =
If the third generation has Y offspring and the ith sub
Lab 1
Greg Hunt
January 11, 2017
R code for this Lab note can be found online: http:/www-bcf.usc.edu/~gareth/ISL/data.html
Chapter 2 Lab: Introduction to R
Installing R on your Personal Computer
Download from: http:/cran.mtu.edu/
Basic Commands
x <- c(1,3
Lab 8 Splines and GAM
Xuefei Zhang
March 10, 2017
We begin by loading the ISLR library, which contains the Wage data.
library(ISLR)
attach(Wage)
Polynomial Regression and Step Functions
fit=lm(wage~poly(age,4),data=Wage)
coef(summary(fit)
#
#
#
#
#
#
Esti
Lab 7
Greg Hunt
February 23, 2017
Subset Selection Methods
Here we apply the best subset selection approach to the Hitters data. We wish to predict a baseball players
Salary on the basis of various statistics associated with performance in the previous ye
Lab 3: Principal Components Analysis
Greg Hunt
January 23, 2017
PCA Viewpoint
At its heart PCA is a dimensionality reduction method. That means it takes the variables we measure
X1 , . . . , XN and looks to find some other variables Y1 , . . . , YM where
Lab 6
Xuefei Zhang
February 17, 2017
The Validation Set Approach
We explore the use of the validation set approach in order to estimate the test error rates that result from
fitting various linear models on the Auto data set. Before we begin, we use the s
Stats 415 Lab 4: LDA and QDA
Xuefei Zhang
February 3, 2017
The Stock Market Data
We begin by examining some numerical and graphical summaries of the Smarket data, which is part of the
ISLR library. This data set consists of percentage returns for the S&P
Lab 5
Greg Hunt
February 8, 2017
Logistic Regression
Logistic regression is one of the most basic and widely used method for classification. As the name implies
its application in R mimics that of linear regression. However instead of predicting the Yi as
Statistics 500: Statistical Learning I: Regression
Fall of 2017
Class 4:00-5:30 MW in MLB AUD 4
Instructor Information:
Instructor:
Office:
e-mail:
Lectures and Homework:
Office hours:
Brian Thelen
443 West Hall
[email protected]
Posted on Canvas
5:30-6:
Statistics 250 Syllabus Fall 2017
Statistics are ubiquitous in life, and so should be statistical reasoning.
Alan Blinder, former Federal Reserve vice chairman and Princeton academic. Inside the List, NYTimes.
Think analytically, rigorously, and sy