State whether the following statements are True or False.
(16=6)
1. The SSR indicates how much of the total variability in the dependent variable is
explained by the regression model. TRUE
2. When we want to use one variable to predict another and use the
1.
The hypothesis tested:
H0 : = = 120
H1 : = 120
Z =
X
/ n
=
122.5120
12/ 49
= 1.46
At /2 = 0.05/2 = 0.025(since it is two tailed), critical value from the normal distribution tables
= 1.96
Since 1.46 < 1.96, there is sufficient evidence to reject the c
1
Provide statistical evidence for each question.
Use Excel for calculations and generating tables, charts, histograms.
Questions
4. Online financing companies are concerned about their competitiveness in
terms of loan dis/approval times. The approval pro
1.
a) Probability distribution of X.
X
P(x)
0
114/1676
= 0.0680
1
186/1676
= 0.1110
2
336/1676
= 0.2005
3
251/1676
= 0.1498
4
316/1676
= 0.1885
5
231/1676
= 0.1378
6
149/1676
= 0.0889
7
33/1676
= 0.0197
8
60/1676
= 0.0358
b) Probability that a person rela
1.
a) True. The probability of an event taking place and the probability of that event not taking
place is impossible.
b) False. If a variance of a data set is zero it implies that all the observations in the data are
identical and not necessarily zero.
c
1
MAT 150 SLP 5 Assignment and Template
I affirm that this assignment contains all original work. I am familiar with Trident Universitys
Academic Integrity policy located in the Trident Policy Handbook. I affirm that I have not engaged
in direct duplicati
1.
a) Probability distribution of X.
X
P(x)
0
114/1676
= 0.0680
1
186/1676
= 0.1110
2
336/1676
= 0.2005
3
251/1676
= 0.1498
4
316/1676
= 0.1885
5
231/1676
= 0.1378
6
149/1676
= 0.0889
7
33/1676
= 0.0197
8
60/1676
= 0.0358
b) Probability that a person rela
2.
The three mean differences that are evaluated by each of the three hypothesis tests that make up a
two factor ANOVA, mean difference of factors the first and the second factors, and the mean
difference of the interactions of the two factors.
The hypoth
a. Overall mean and SD for males and females from all three experiment groups (simple, GNG,
and Choice).
Simple data
Simple
0.7624
38
0.0754
66
0.3735
0.301
0.9545
81
Mean
Standard Error
Median
Mode
Standard Deviation
Mean = 0.7624, SD = 0.9546
GNG data
G
The first plot r = 0.82, the second on the right of it r = 0.00(horizontal line)
The third one (right below the first) r = - 0.92. The fourth one, on its right, r = - 0.76. The last one, r
= 0.66
Based on scatter plot you would expect the correlation to b
MTHM024/MTH714U
Group Theory
Revision Notes
Autumn 2010
Group theory is a central part of modern mathematics. Its origins lie in geometry
(where groups describe in a very detailed way the symmetries of geometric objects)
and in the theory of polynomial eq
26
Tensors
It may seem obvious that the quantitative description of physical processes cannot
depend on the coordinate system in which they are represented. However, we may
turn this argument around: since physical results must indeed be independent of
th
GROUP ACTIONS
KEITH CONRAD
1. Introduction
The symmetric groups Sn , alternating groups An , and (for n 3) dihedral groups Dn
behave, by their very definition, as permutations on certain sets. The groups Sn and An
both permute the set cfw_1, 2, . . . , n
DIHEDRAL GROUPS II
KEITH CONRAD
We will characterize dihedral groups in terms of generators and relations, and describe
the subgroups of Dn .
1. Abstract characterization of Dn
The group Dn has two generators r and s with orders n and 2 such that srs1 = r
HOMOMORPHISMS
KEITH CONRAD
1. Introduction
In group theory, the most important functions between two groups are those that preserve the
group operations, and they are called homomorphisms. A function f : G H between two groups
is a homomorphism when
f (xy
Group Actions
Patrick J. Morandi
There are a number of results of group theory presented in Herstein [1] (the counting
principles in Sections 2.5 and 2.11, Cayleys theorem in Section 2.9 and the Sylow theorems
of Section 2.12, among others) whose proofs f
Vectors & Matrices : suffix notation
A common early vectors question is prove that a (b c) = (a c)b (a b)c, and a typical
first attempt will go something like:
Since x y = (x2 y3 x3 y2 , x3 y1 x1 y3 , x1 y2 x2 y1 ), the first components of each side are
L
Some stuff about integrals and differentials
Line Integrals
Suppose that we have a small bead on a wire. If a constant force pushes the bead along the wire,
then the work done by the force is given by the formula force distance. If the force varies
as the
Arc-length, curvature, torsion, etc.
Suppose that I go for a drive around town, trying to decide which is the scariest corner. If my speed
isnt constant then I might find it hard to tell. For example, if I compare a shallow bend driven at
60mph to a sharp
Jacobians
Suppose we wish to integrate
Z
cos(x2 + y 2 ) dA, where A is the region between two quarter-circles:
A
y
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
A
1
2
x
We decide to change to polar coordinates, by setting x = r cos , y = r s
Hyperbolic functions
CRTM, 2008
Several paths may be followed that each culminate in the appearance of hyperbolic functions. I am
going to define the functions first.
cosh x =
sech x =
ex + ex
;
2
1
;
cosh x
sinh x =
cosech x =
ex ex
;
2
1
;
sinh x
tanh x
Groups : homomorphisms
Suppose that we have two groups, (G, ) and (H, ?). Treating these just as sets, there would be
many maps between them, as we could freely send things anywhere. However, a homomorphism
attempts to preserve some structure: it respects
A Discontinuous but Integrable Function
Will Rosenbaum
Updated: January 15, 2013
Department of Mathematics
University of California, Los Angeles
In this note, we give an example of a function that is discontinuous on a dense subset of
R, but is nonetheles
Find the matrix of the linear transformation T : R3 R3 if
1
1
T 2 = 1
3
1
2
0
T 3 = 1
4
2
0
1
T 2 = 2
3
2
Let us denote the standard basis vectors with
1
e1 = 0
0
0
e2 = 1
0
0
e3 = 0.
1
We will prove in class that if T is linear, then th
group actions and homomorphisms
CWoo
2013-03-21 15:23:08
Notes on group actions and homomorphisms
Let G be a group, X a non-empty set and SX the symmetric group of X,
i.e. the group of all bijective maps on X. may denote a left group action of G
on X.
1.
Chapter 6
Eigenvalues and Eigenvectors
Po-Ning Chen, Professor
Department of Electrical and Computer Engineering
National Chiao Tung University
Hsin Chu, Taiwan 30010, R.O.C.
6.1 Introduction to eigenvalues
6-1
Motivations
The static system problem of Ax
Greens theorem in the plane
Greens theorem in the plane. For functions P (x, y) and Q(x, y) defined in R2 , we have
I
ZZ
Q P
dx dy
(P dx + Q dy) =
x
y
C
A
where C is a simple closed curve bounding the region A.
Vector Calculus is a methods course, in whi
ST334 ACTUARIAL METHODS
version 2016/03
These notes are for ST334 Actuarial Methods. The course covers Actuarial CT1 and some related financial
topics.
Actuarial CT1 is called Financial Mathematics by the Institute of Actuaries. However, we reserve the te
Lecture notes on: Actuarial Models
Ronnie Loeffen
November 26, 2016
Contents
1 Discrete time Markov chains
1.1 Stochastic processes and the Markov property .
1.2 Discrete time Markov chains . . . . . . . . . . .
1.3 How to construct a discrete time Markov