Chapter 1: Introduction to Probability and Counting
A basic goal of science is to describe and explain some process or phenomenon. Often, this
entails making a prediction of the outcome of some type of experiment. If this outcome is an
observed value such
STAT 4710/7710 Assignment 5
Due Monday June 19
1. (60 points total) The two most common types of errors made by programmers are syntax
errors and errors in logic. For a simple language such as BASIC the number of such
errors is usually small. Let X denote
STAT 4710/7710-03 Fall 2016 Exam 1
Name _
Show all work on exam. Extra scratch paper is available if necessary. Round to four decimal
places if necessary. Total 100 points.
1. (12 points total) A committee of size 5 is to be randomly selected from a group
Exam 1 Topics
Section 1.2
Give the sample space S.
List the outcomes in a given event, including intersections (AND) and unions (OR).
Determine if events are mutually exclusive.
Section 1.3
Use the classical formula P [A] =
n(A)
n(S)
when all outcomes are
Chapter 2: Some Probability Laws
2.1: Axioms of Probability
The axioms of probability govern how probabilities behave and define their properties. A
mathematical system has to begin with definitions and axioms that are assumed to be true. They
do not have
STAT 4710/7710 Assignment 7
Due Friday June 23
1. (40 points total) The following numbers represent a random sample from a normal
distribution with variance of 16 and unknown mean :
7.64
6.38
6.06
5.59
2.03
1.17
8.42
-6.83 2.25
5.78
7.56
4.33
a. (10 point
STAT 4710/7710 Assignment 4
Due Friday June 16
Each part is worth 5 points, for a total of 100 points.
1. For the continuous density function f (x) =
c
x
0 < x < 1 find the following:
a. c
b. F(x)
c. E[X]
d. Var(X)
e. P[.25 < X < .5]
f. P[X > -1]
g. P[X <
Chapter 3: Discrete Distributions
The values of a random variable are determined by chance. A random variable is what is being
observed or measured in an experiment. Random variables are usually either discrete or
continuous.
3.1: Random Variables
Typical
Chapter 4: Continuous Distributions
A continuous random variable does not have a countable number of possible values. The
probability of a single point is 0, but probabilities are defined for intervals of real numbers. The
sample space is one or more inte
STAT 4710/7710 Assignment 6 Solutions
1.
5|3
6|1225778
7|11134444666778999
8|0112224577788
9|0123455667
10| 0
2. n = 48, so we use 6 classes. The unit is .1, so the half-unit is .05. The range is 10 5.3 = 4.7,
so the length will be 4.7/6 = .8
Category
Bou
STAT 4710/7710 Assignment 5 Solutions
1.
a.
P[X = 0 and Y = 0] = .400
b. P[X 1 and Y 1] = P[X = 1 and Y = 0] + P[X = 1 and Y = 1] + P[X = 2 and Y = 0]
+ P[X = 2 and Y = 1] + P[X = 3 and Y = 0] + P[X = 3 and Y = 1]
= .100 + .040 + .020 + .010 + .005 + .004
STAT 4710/7710 Assignment 3 Solutions
1. a. (2 points) Sum f(1) through f(7) to get .97. Then f(8) = 1 .97 = .03. This should
be the last entry in the table.
b. (3 points)
X
F(x)
1
.02
2
.05
3
.10
4
.30
5
.70
6
.90
7
.97
c. (2 points) P[3 X 5] = P[X 5] P[
STAT 4710/7710 Assignment 2 Solutions
1. (10 points total, 5 points each) When a computer goes down, there is a 75% chance that it
is due to an overload and a 15% chance that it is due to a software problem. There is an
85% chance that it is due to an ove
Assignment 1 Solutions
2
=0.04
50
1.
2.
b.
cfw_h, mh, mmh, mmmh, mmmmh, mmmmm
c.
A1 = cfw_mh
d.
They are not mutually exclusive because exactly 2 is a special case of at
most 2.
A2 = cfw_h, mh
17 3
(
5 )( 0 ) 6188
P [ accepted ] =P [ 5 are not defective ]
STAT 4710/7710 Summer 2017 Exam 1 Solution
Name _
Show all work on exam or scratch paper. Round to four decimal places if necessary. Total 100
points.
1. (10 points) At a local blood bank, 67% of donors are paid, while the remaining donate for
free. If a
STAT 4710/7710-03 Fall 2016 Exam 1
Name _
Show all work on exam. Extra scratch paper is available if necessary. Round to four decimal
places if necessary. Total 100 points.
1. (12 points total) A committee of size 5 is to be randomly selected from a group
Elements of a Designed Experiment
CRD
Multiple Comparisons of Means
RBD
Factorial Experiments
Introduction to Probability and Statistics II
I
Instructor: Cheng Dong
I
Office: Middlebush 27
I
Office hours: TuTh: 9:10am-10:40am
I
Email: [email protected]
(25pts) 2. Use the method of variation of parameters to solve the initial value problem
3;" + my + 253; = f(t) ,
y(0) = 0, y(0) = 1.
as: -5
cfw_ve lae k
m 8 S ~x IUK
Nll 51 -591? we 2 we
21 "
l 2
l _ 5: F0
w m, 3 n MW as: m A
a -e" rm -s:.[ + 91;" (w
Vs
Math4100 - Exam 3
Your Name: (PRINT) CWshw MW
Your ID: \4C0%6b6\
(2513138) 1. Using the Euler method to nd the approximate value of the solution at
X=0.1, 0.2,
y 332:2, y(0)=2, 11:01
la %o*\f\L0 U31
3': 5 (VIN 2. (25 pts) Solve the initial value probl
Exam #1 All sections
February 20, 2012 100 points
"' i 1 CN 3' Smdent#1WMSect.ortime:m105%\r
lth the name of our Instructor:
Jacob 513$? k Trevor Nilatpal Haiying Chang
gassett Orme Liang Oswald Sanyal Wang Xu
Instructions
0 MATERIAL: This exam covers sec
Statistics 2500 Exam #2 All sections
SP2012 / Form F4 March 12, 2012 100 points
NamCILMVlShl/lf Campbili Student #: l4l01il 4i Sect. or time: S
Circle the name of your Instructor:
Instructions
0 MATERIAL: This exam covers sections 5.1 5.5 and 6.1
(25pts) 2. Determine Whether or not the equation is exact. Find the general solution.
1.13
(3ye )dzc+mdy=0.
dM 3
l '_"'1.
Mat-:12 4
N emdr
CLN
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K N K K 14 Math4100 Exam 1
Your Name: (print) WWW WWM 8 g
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Statistics 2500 Exam #3 I ' All sections
SP2012 / Form F1 April 16, 2-012 100 points
l l7? Student #:M Sect. or time: fw-
_ Instructions
Material: Sections 7.1 7.4, 8.1 8.6, and 9.1 w 9.3.
The last question on the exam is 06. It is on page #4.
P
*1. Data was gathered for all teams (28 total) from the 1994 National Football League (NFL) regular season. First we will
look at a simple linear regression using the number of interceptions (INT) to try and predict the total number of points a
team score
\
C11. A multiple regression model was fit for y using 3 independent variables (x1, x2, and x3). Below is the
correlation matrix for the variables as well as the output for the fitted model. Answer the following questions.
Correlations: y! x1, x2, x3 Pred
fig
Q2. A pharmaceutical company wished to test the effectiveness of a new allergy medication. There were two
independent factors of interest: gender (male or female) and ago (young, middle, and old). The ANOVA table
and multiple comparisons are given bel
17-18
(1)
Activity Pool
Direct labor related
Inspection related
Total variable
O/H costs
Traceable
Costs
$197,200
144,000
Total
Driver Units
68,000 DLH
80,000 IN
$341,200
Variable
Flims
_
Total
Overhead Driver Units
Amount Driver Units
$2.90/DLH
8,000
$ 2