Stat 224/324
October 14, 2015
Assignment #6 Solutions
Soil Problem
1. Since the question is whether the mean is different than 4%, we want a two-sided alternative, so we would
want to test:
H0 : = 4%
vs.
HA : 6= 4%.
2. With very little data, histograms wo
STAT 224/324
Second Midterm Exam
November 11th, 2015
Name:
Discussion Section/Time:
For instructors use:
You are allowed two 8.5 by 11 inch pieces of paper, both sides, for
notes, and you may use a calculator. Laptops, tablets, and smartphones are not al
Stat 224/324
March 9, 2016
Assignment #6 Due Friday, March 18, by 4pm
*Submit your homework to Hyebin Songs mailbox anytime prior to the due date/time. The mailboxes are
to the left as you enter the Medical Science Center (1300 University Ave.) from the m
Stat 224/324
March 2, 2016
Assignment #5 Solutions
1. (a) Since it is bad if the packages are either too heavy or too light, we need a two-sided alternative. If is
the population mean package weight, then our hypotheses might be:
H0 : = 8oz
HA : 6= 8oz
(b
Stat 224/324
March 3, 2016
Assignment #5 Due Friday, Mar. 11, by 4pm
*Submit your homework to Hyebin Songs mailbox anytime prior to the due date/time. Please put your homework in the correct folder which corresponds to your discussion section. The mailbox
Stat 224/324
Feb. 22, 2016
Assignment #4 Due Friday, Mar. 4, by 4pm
*Submit your homework to Tong Lis mailbox anytime prior to the due date/time. (The mailboxes are to the
left as you enter the Medical Science Center (1300 University Ave.) from the main U
Data Analysis Course
Regression - Summary
Draft: January 18, 2016
Regression - Summary
1. Regression
We are interested in exploring the relationship between two variables y (the response) and x (the predictor).
If the model is linear we can express it as:
Data Analysis Course
Multiple Independent Populations - Summary
Draft: January 18, 2016
Comparing Multiple Independent Populations - Summary
1. ANOVA
If we have simple random samples from more than two treatments (say, t treatments), and wish to test:
H0
Raskutti Statistics/Mathematics 309
Solutions to Practice Midterm 2
1. An earthquake of magnitude M releases energy X such that M = loge X. The earthquake magnitude has
an exponential distribution with mean 2.
(a) (3 points) Find E(M ) and the CDF of M .
Raskutti Statistics/Mathematics 309
Solutions to Practice Midterm 2
2
Since ex is an even function,
Z
E[ Y ] =
0
1
2
Z
2
ex dx
2
ex dx
Z
1p
2
2
ex dx
. /
2
2
1p
. /.
2
=
=
=
where
the last equality follows since we are integrating the density of N (0, (
Statistics/Mathematics 309
Raskutti
March 1, 2016
Assignment #7 Due Thursday, March 10, 2016, by 5:15 P.M.
Turn in homework in lecture, discussion, or your TAs mailbox (just inside the main entrance of MSC, 1300
University Avenue)
1. Let IA denote the ind
Statistics/Mathematics 309
Raskutti
March 4, 2016
Assignment #8 Due Thursday, March 17, 2016, by 5:15 P.M.
Turn in homework in lecture, discussion, or your TAs mailbox (just inside the main entrance of MSC, 1300
University Avenue)
1. If X Exponential(), f
Raskutti Statistics/Mathematics 309
Practice Midterm 2
Name:
1. An earthquake of magnitude M releases energy X such that M = loge X. The earthquake magnitude has
an exponential distribution with mean 2.
(a) (5 points) Find E(M ) and the CDF for M .
(b) (5
Raskutti Statistics/Mathematics 309
Solutions to Practice Midterm 2
(a) (5 points) Find the CDF F (x) = P (X x) for the random variable X.
Rx
Solution: By definition F (x) = f (z)dz. Hence for x < 0, F (x) = 0 and for x > 0, F (x) =
Rx
z 2 dz. Therefore
0
Statistics/Mathematics 309
Raskutti
March 15, 2016
Assignment #9 Due Thursday, March 31, 2016, by 5:15 P.M.
Turn in homework in lecture, discussion, or your TAs mailbox (just inside the main entrance of MSC, 1300
University Avenue)
1. Find the moment gene
Raskutti Statistics/Mathematics 309
Solutions to Practice Midterm 2
(d) (5 points) Find the PDF for X(100) (You may express your answer in terms of the standard normal
CDF).
Solution: The PDF for X(100) has the form
f100 (x) = 100f (x).(F (x)99 ,
where f
Statistics/Mathematics 309
Raskutti
February 16, 2016
Assignment #5 Due Thursday, October 8, 2015, by 5:15 P.M.
Turn in homework in lecture, discussion, or your TAs mailbox (just inside the main entrance of MSC, 1300
University Avenue)
1. Let X Geometric(
Statistics/Mathematics 309
Raskutti
February 24, 2016
Assignment #6 Due Thursday March 3, 2016, by 5:15 P.M.
Turn in homework in lecture, discussion, or your TAs mailbox (just inside the main entrance of MSC, 1300
University Avenue)
1. The PDF for the fol