1. In a study for hangover recovery, ten students were given equal amounts of alcohol and then
given either treatment A or B. Alcohol in the blood was measured one hour later. The data
is below (each sample is ordered for your convenience).
Treatment A: 0
STAT464 Homework #3
due Wednesday, 9/17
1. The following values were sampled independently from F (x).
0.8
0.7
4.1
0.9
2.5
(a) Use the Kolmogorov-Smirnov test statistic to test H0 : F (x) = F0 (x) versus Ha : F (x) =
F0 (x), where F0 (x) = 1 ex is the cdf
STAT464 Homework #5
due Monday, 9/29
In a study to see if cloud seeding aects rainfall, the following samples of rainfall were observed:
seeding: .74 .54 1.25 .27 .76 1.01 .49 .7
no seeding: .25 .36 .42 .16 .59 .66
Test to see if seeding increases rainfal
STAT464 Homework #8
due Wednesday, 10/29
1. (Adapted from Higgins, Ex4.1 ) For the data in the table below,
a) Obtain the permutation distribution of the mean of the dierences. There are 16 possible permutations. For each one, give the dierence for each p
STAT464 Homework #6
due Wednesday, 10/15
1. (Adapted from Higgins, Ex3.1 ) The data in exercise 3.1.dat are samples from three simulated distributions. The data can be read into R with the following command:
x=read.table("exercise 3.1.dat", header=T, sep=
STAT464 Homework #1
due Wednesday, 9/3
1. In ten binomial trials with success probability 1/3, nd the probability of more than four
successes.
If X is the binomial variable considered here, then
P (X > 4) = 1 P (X 4) = 1
4
(10) ( 1 )x ( 2 )10x
x=0
x
3
3
STAT464 Homework #9
due Wednesday, 11/5
(Adapted from Higgins, Ex4.7 ) The data in hay.dat are dry matter contents (in kilograms) of hay
obtained from experimental plots. The experiment was designed as a randomized complete block
with six blocks, and the
STAT464 Homework #2
due Wednesday, 9/10
1. (adapted from Higgins, Ex1.3 ) Consider again the exam score data from Homework 1. R
software will be needed for these questions.
0
65
70
5
75
80
10
85
90
15
95
(a) Create either a histogram or a box plot of the
STAT464 Homework #7
due Wednesday, 10/22
(Adapted from Higgins, Ex3.6 ) The data in exercise 3.6.dat are the head injury readings for
driver-side crash dummies for various classes of vehicles. The vehicle types are coded as 1=Compact,
2=Heavy, 3=Light, 4=
Practice #1
1.5 Suppose we assume that the population distribution under H0 is symmetric so that .5 = .
Without looking at the data to check the validity of this assumption, we apply the binomial
test and the CLT test. Suppose it turns out that 39 data va
STAT464 Homework #2
due Wednesday, 9/10
1. (adapted from Higgins, Ex1.3 ) Consider again the exam score data from Homework 1. R
software will be needed for these questions.
(a) Create either a histogram or a box plot of the data (include it here). Comment
STAT464 Homework #4
due Wednesday, 9/24
1. (Taken from Higgins, Ex2.1 ) A certain data set has eight distinct observations, four from
each treatment, and all of the observations from treatment 1 are bigger than the observations
from treatment 2. What is t
Learning R
Install R
You can find the most recent version of R at http:/www.r-project.org/
The website will require you to choose a CRAN Mirror. the idea is to find the location geographically
closest to you. Right now the closest option is probably to
Homework 2 Solutions
Solutions for the Additional Problems
1(a) Rayleigh samples using inverse cdf method
Algorithm
for i=1 to 1000
1. Generate Ui U nif orm(0, 1)
p
2. Obtain Zi = 2 2 log(1 Ui ) which is the inverse CDF.
sigma <- sqrt(2)
u <- runif(1000)
STAT 440 SPRING 2017
HOMEWORK 1 SOLUTIONS
1. ( One way to do (a)(b) )
Z
n
E(X ) =
xn f (x) dx
Z0
(3t)n et dt
=
(x 3t)
0
n
= 3 (n + 1)
= 3n n!
(a) E(X) = 3
V ar(X) = E(X 2 ) E(X)2 = 9
(b) E(X 3 ) = 162
(c) P (X < x) = F (x) = 1 ex/3
so P (X [2, 10]) = F
introR: Introduction to Programming with R
Lab 1: Vectors, matrices and some operations
Author(s): Andrea S Foulkes
STAT 440
Ben Shaby
This material is part of the statsTeachR project
Made available under the Creative Commons Attribution-ShareAlike 3.0 Un
introR: Introduction to Programming with R
Lab 2: More on objects
Author(s): Andrea S Foulkes
STAT 440
Ben Shaby
This material is part of the statsTeachR project
Made available under the Creative Commons Attribution-ShareAlike 3.0 Unported License:
http:/
STAT 440: Homework 4
Due: 2/16/2017
For all problems, turn in the full R-code you used to answer the questions. In a separate file, use knitr to
report any analytic derivations you made. Clearly mark where your code switches from one problem to the
next.
STAT 440: Homework 1
Due: 1/19/2017
1. Let X be an exponential random variable with rate parameter 3. Then X has probability density
function
1
f (x) = ex/3 for x 0.
3
(a) Find the mean and variance of X.
(b) Find the 3-rd moment of X: E(X 3 ).
(c) Find P
Practice #2
1. (Adapted from Higgins, Ex4.12 ) Three varieties of soybeans were tested for yields in a randomized complete block design (RCBD). The varieties are known to have varying levels of
susceptibility to iron deciency. The data are average chloros
STAT464 Homework #11
due Wednesday, 12/3
1. (Adapted from Higgins, Ex5.1 and Ex5.2 ) The table below shows x = height and y = weight
for n = 3 individuals.
Height
Weight
68
145
70
155
74
160
(a) Find the permutation distribution of the slope of the least
Practice #2
1. (Adapted from Higgins, Ex4.12 ) Three varieties of soybeans were tested for yields in a randomized complete block design (RCBD). The varieties are known to have varying levels of
susceptibility to iron deciency. The data are average chloros
STAT464 Worksheet
This worksheet is adapted from Exercise 2.4 from our text. Completing this will require R software.
The dataset is carapace.dat, available in our ANGELs data folder. The values are carapace
lengths (in mm) of craysh recorded from two sec
STAT464 Homework #1
due Wednesday, 9/3
1. In ten binomial trials with success probability 1/3, nd the probability of more than four
successes.
2. Assume that for a particular tire brand, the probability of wearing out before 30,000 miles is
0.25. For some
STAT464 Homework #3
due Wednesday, 9/17
1. The following values were sampled independently from F (x).
0.8
0.7
4.1
0.9
2.5
(a) Use the Kolmogorov-Smirnov test statistic to test H0 : F (x) = F0 (x) versus Ha : F (x) =
F0 (x), where F0 (x) = 1 ex is the cdf
STAT464 Homework #5
due Monday, 9/29
In a study to see if cloud seeding aects rainfall, the following samples of rainfall were observed:
seeding: .74 .54 1.25 .27 .76 1.01 .49 .7
no seeding: .25 .36 .42 .16 .59 .66
Test to see if seeding increases rainfal
STAT464 Homework #4
due Wednesday, 9/24
1. (Taken from Higgins, Ex2.1 ) A certain data set has eight distinct observations, four from
each treatment, and all of the observations from treatment 1 are bigger than the observations
from treatment 2. What is t
STAT464 Homework #7
due Wednesday, 10/22
(Adapted from Higgins, Ex3.6 ) The data in exercise 3.6.dat are the head injury readings for
driver-side crash dummies for various classes of vehicles. The vehicle types are coded as 1=Compact,
2=Heavy, 3=Light, 4=
STAT464 Homework #6
due Wednesday, 10/15
1. (Adapted from Higgins, Ex3.1 ) The data in exercise 3.1.dat are samples from three simulated distributions. The data can be read into R with the following command:
x=read.table("exercise 3.1.dat", header=T, sep=