Midterm 1 - 09/28/2016
Name:
ID:
Problem 1:
Problem 2:
Problem 3:
Problem 4:
Problem 5:
Bonus points
Total:
out
out
out
out
out
of
of
of
of
of
20
18
40
12
10
out of 100
1. This test consists of 10 pages. Check that you have all pages. The tables are provi
Homework 2
1. This problem will be performed in R using the R commands.
(a) To fit a simple linear regression model relating games won (y) to yards gained rushing by
opponents (x8 ), we first need to visualize the data and see whether a linear relationshi
Homework 1
1. We have the following model
yi = 0 + 1 xi i , i = 1, 2, ., n,
where
yi is the response, that is the production after taking a training for the ith person
0 , 1 are the unknown parameters, the regression coefficients
xi is the predictor va
Homework 2
Due 09/07/2016
1. Problem 2.1: Table B.1 gives data concerning the performance of the 26 National Football
League teams in 1976. It is suspected that the number of yards gained rushing by opponents
(x8 ) has an effect on the number of games won
Review for Midterm 1
1. The flow rate y (m3 /min) in a device used for air-quality measurement depends on the pressure drop x
(in. of water) across the devices filter. Suppose that for x values between 5 and 20, the two variables
are related according to
Review for Midterm 1
1. The flow rate y (m3 /min) in a device used for air-quality measurement depends on the pressure drop x
(in. of water) across the devices filter. Suppose that for x values between 5 and 20, the two variables
are related according to
Homework 1: Due 08/31/2016
1. Problem 1.11 from KNNL book: The regression function relating production
output by an employee after taking a training program (y) to the production output
before the training program
1
Chapter 2: Simple Linear Regression
The model: y = 0 + 1 x + , where y is the response variable, 0 and 1 are the unknown regression coefficients,
x is the predictor variable, assumed to be constant, and are uncorrelated and normally distributed errors
STA 4033
Mathematical Statistics
with Computer Applications
Lecture 16
Brett Presnell
Department of Statistics
University of Florida
11 June 2001
Contents
6.3 Formulas for the LSEs . . . . . . . . . . . .
6.4 Standard Errors and Estimating the Variance
6.
Name Date I Block
UConn Statistics
Final Review
1.) if a peanut M&M is chosen at random, the chances of it being of a particular color are shown in the
following table:
COLOR
PROBABILITY
The probability of randomly drawing a blue peanut M&M is:
a.) 0.1
b.
ST511 MIDTERM EXAM I Name: 0 LU ON
10/06/2014
[Total Time: 110 min] Max Points: 100
1. Suppose that A, B, C be three independent events with P(A) = .1, P( B) = .2, and 13(0) = .3.
(a) Find P([A U B] cfw_1 C). (10pts)
4 a) P:
uia 5,1316. iwiqnwlwk 7) (FY-Q
I
ST511 SAMPLE FINAL EXAM Name: _
12/09/2014 [Total Time: 2 hrs] Total p0ints=112; Max Score: 100
1. At a certain university, 40% of juniors and 30% of seniors have a GPA of 3.5 or more. Further, of
the students in their junior-senior classes, 45% are jun
ST 511
Homework 7 Solution
5.11 can be replaced by s. We will use normal distribution.
> 9.02 + c(-1, 1)*qnorm(0.95)*1.12/sqrt(40)
[1] 8.728717 9.311283
5.18 Since we have to use s to estimate , we will use t distribution.
(a) Since p < , we reject the nu
ST 511
Homework 8 Solution
8.6
(a) There seems to be a difference, possibly between device A and D.
(b) We reject the null hypothesis and conclude that there is difference among the means.
> wide <- read.table(header = T, text = '
device sample1 sample2 s
ST 511
Homework 3 Solution
4.10 HHH, HHT, HT H, HT T, T HH, T HT, T T H, T T T
4.13
a. 1/6
b. 1/2
c. 1/2
d. 2/3
4.17
a. 0.15
b. 0.25
c. 0.75
d. 0
4.20
a. Independent: none. In all pairs, knowing one event gives information about the other event.
b. Mutual
ST 511
Homework 1 Solution
2.9 Time magazine.
a. Average Class of 1924 Yalemans salary
b. Unlikely to produce a representative sample.
c. 1) Converage bias (unrepresentative sampling frame): administration might keep more records
of those who are better o
Lecture 16
Consistency
Unless mentioned otherwise in the next few lectures, we assume that cfw_Xn is a sequence of iid samples from P , , and will present some basic results in asymptotic statistics, i.e. large sample theory. Definition 1 Tn = T (X n ) i
Lecture 12
Some Extensions of Neyman-Pearson Theory
12.1
One-sided hypotheses and monotone likelihood ratios
Definition 1 F = cfw_f (|), is said to have a monotone likelihood ratio (MLR) for f (x|1 ) a sufficient statistic U if for any 0 < 1 , the ratio
Lecture 11
Neyman-Pearson Theory
Neyman-Pearson theory sets a foundation for hypothesis testing. It enhances our understanding of the trade-off between type I and type II errors. Definition 1 For (0, 1), let T be the set of all level- tests (including ran
Lecture 7
Maximum Likelihood
Maximum likelihood has been the most extensively used frequentist method in point estimation. Unlike empirical frequencies introduced in Lecture 6, maximum likelihood is a fully model-based approach. See Efron's Wald Lecture p
Lecture 10
Likelihood Ratio Tests
In this lecture, a basic framework of hypothesis testing will be presented, followed by an introduction to likelihood ratio tests.
10.1
Basic elements in hypothesis testing
Data model: X f (x|), x X , . Parameter space d