Chapter III:
Numerical Summary Measures
Chapter Outline
3.1 Measures of Central Tendency
Mean
Median
Mode
3.2 Measures of Dispersion
Range
Deviance
Variance and standard deviation
Coefficient of variation
Interquartile range
Measurement Scales
Measurement
UNIVERSITY OF TECHNOLOGY, JAMAICA
COLLEGE MATHEMATICS 1A (MAT 1044)
WORKSHEET # 8: FINANACIAL MATHEMATICS
1.
Aisha invests EC$50,000 at 12% per annum. Find the accrued amount after eight
years if the interest is compounded
(a) annually
2.
(b) quarterly
(c
UNIVERSITY OF TECHNOLOGY, JAMAICA
FACULTY OF HEALTH AND APPLIED SCIENCE
TUTORIAL SHEET #5: GRAPHS
COURSE: COLLEGE MATHEMATICS
1.
2 x 2 5 x 6 for 4
Plot the graph of the function y
x 2
Using your graph :
2.
(i) find the minmum value of y
(ii) solve the equ
1
UNIVERSITY OF TECHNOLOGY , JAMAICA
TUTORIAL SHEET #3 : INDICES
AY: 2009-2010
MODULE : College Mathematics
In Question 1, 2 and 3 evaluate or simplify without using calculators
1.
2.
i)
5a 4 b 3 (a 2 b 5 ) 2
(ii)
2 n 8 2n n
(iii)
x4 ( y2 z3 )4
(x2 z 5 )2
1
UNIVERSITY OF TECHNOLOGY , JAMAICA
WORKSHEET SHEET #4 : LOGARITHMS
AY: 2009 - 2010
MODULE : COLLEGE MATHEMATICS
Definition:- The logarithm of a positive number N to a given base a is power to which
the base must be raised to obtain the number. That is i
UNIVERSITY OF TECHNOLOGY, JAMAICA
TUTORIAL SHEET #7 : MATRICES
AY: 2009-2010
1.
College Mathematics
1 2
Given that A
0
B
1 3
1
2 3
3
5 2
C
1
1 1
1 2 0
1 3 3
2 3 1
D
Find the following:
2.
(a)
2 A 3B
(b)
3 A 2C
(e)
A1
(f)
B
1
(c)
AB
(g)
C
1
(d)
BD
(h)
D
1
Student Name: Curtis Smith (AC1102853)
Student Identification Number: 2132096
Course Number and Title: MA240 College Algebra
Assignment Number and Title: Assignment 8_08
Date of Submission: January 16, 2016
a. Use the numbers shown in the bar graph below
Student Name: Curtis Smith (AC1102853)
Student Identification Number: 2132096
Course Number and Title: MA240 College Algebra
Assignment Number and Title: Assignment 4_04
Date of Submission: January 16, 2016
Question 1
The function P (t) = 145e-0.092t mode
1.
INTRODUCTION
Data obtained from observations collected sequentially over time are extremely
common. For example:
In business, we observe weekly interest rates, daily closing stock prices,
monthly price indices, yearly sales figures.
In meteorology, w
1.5
Serial Dependence
Recall that the y ' s are not independent but are serially dependent. We can describe
the nature of the dependence using a set of autocorrelations.
1.5.1 Autocorrelation
( y1,., yn ) on a time series, we can form n 1 pairs
namely, (
3.4
Partial Autocorrelation Function (PACF)
Consider the general statement:- the partial correlation coefficient between X and Y
with dependence on a third variable Z removed is given by
Corr ( X , Y | Z ) = XY .Z =
XY XZ YZ
(1 )(1 )
2
XZ
2
YZ
In our cas
1.
INTRODUCTION
Data obtained from observations collected sequentially over time are extremely
common. For example:
In business, we observe weekly interest rates, daily closing stock prices,
monthly price indices, yearly sales figures.
In meteorology, w
3.
MODELS FOR STATIONARY TIME SERIES
The process cfw_Yt is called a linear process if it has a representation of the form
Yt = +
i Z t i
i =
where:
is a common mean
cfw_ i
cfw_Z t
is a sequence of fixed constants
are independent random variables with
3.3
ARMA
An ARMA model, of order ( p, q ) is defined by
Yt = 1Yt 1 + . + pYt p + Z t + 1Z t 1 + . + q Z t q
(3.3.1)
ie
p
q
i =1
i =0
Yt = iYt i + i Z t i
which is an autoregressive moving average process of order
( p, q )
or an
ARMA ( p, q ) .
In other wo
2.
STATIONARY PROCESSES
We shall describe the fundamental concepts in theory of time series models.
Introduce the concepts of stochastic processes, mean and covariance functions,
stationary processes and autocorrelation functions.
2.1
Stochastic Processes
3.2
Autoregressive Processes
Autoregressive processes as their name suggests regressions on themselves.
A pth order autoregressive process cfw_Yt is given by
Yt = 1Yt 1 + 2Yt 2 + . pYt p + Zt
(3.2.1)
The current value of the series Yt is a linear combina
1.6
Seasonal variation
The time plot should be examined to see which model, whether additive or
multiplicative is likely to give a better description. The seasonal indices
cfw_st
are
usually assumed to change slowly through time so that st st s , where '