Mathematics for Business, Science, and Technology – With MATLAB and Spreadsheet Applications

Mathematics for Business, Science, and Technology – With MATLAB and Spreadsheet Applications
Includes a Comprehensive Treatment of Probability and Statistics Illustrated with Numerous Real-World Examples
Steven T. Karris
Second Edition
Table of Contents
Chapter 1
Numbers and Arithmetic Operations
Number Systems 1-1
Positive and Negative Numbers 1-1
Addition and Subtraction . 1-2
Multiplication and Division 1-7
Integer, Fractional, and Mixed Numbers 1-10
Reciprocals of Numbers . 1-11
Arithmetic Operations with Fractional Numbers . 1-12
Exponents 1-21
Scientific Notation 1-24
Operations with Numbers in Scientific Notation . 1-26
Square and Cubic Roots 1-28
Common and Natural Logarithms 1-30
Decibel . 1-32
Percentages 1-32
International System of Units (SI) 1-33
Graphs . 1-37
Summary 1-41
Exercises 1-46
Solutions to Exercises 1-47
Chapter 2
Elementary Algebra
Introduction . 2-1
Algebraic Equations 2-2
Laws of Exponents . 2-5
Laws of Logarithms 2-8
Quadratic Equations 2-11
Cubic and Higher Degree Equations . 2-13
Measures of Central Tendency . 2-13
Interpolation and Extrapolation 2-15
Infinite Sequences and Series 2-18
Arithmetic Series . 2-19
Geometric Series 2-19
Harmonic Series 2-21ii Mathematics for Business, Science, and Technology, Second Edition
Orchard Publications
Proportions .2-23
Summary .2-24
Exercises .2-28
Solutions to Exercises .2-30
Chapter 3
Intermediate Algebra
Systems of Two Equations 3-1
Systems of Three Equations .3-6
Matrices and Simultaneous Solution of Equations 3-6
Summary .3-25
Exercises .3-29
Solutions to Exercises .3-31
Chapter 4
Fundamentals of Geometry
Introduction .4-1
Plane Geometry Figures 4-1
Solid Geometry Figures 4-17
Using Spreadsheets to Find Areas of Irregular Polygons .4-21
Summary .4-24
Exercises .4-29
Solutions to Exercises .4-31
Chapter 5
Fundamentals of Plane Trigonometry
Introduction .5-1
Trigonometric Functions 5-2
Trigonometric Functions of an Acute Angle .5-2
Trigonometric Functions of an Any Angle 5-3
Fundamental Relations and Identities .5-6
Triangle Formulas .5-12
Inverse Trigonometric Functions .5-14
Area of Polygons in Terms of Trigonometric Functions 5-14
Summary .5-16
Exercises .5-18
Solutions to Exercises .5-19Mathematics for Business, Science, and Technology, Second Edition iii
Orchard Publications
Chapter 6
Fundamentals of Calculus
Introduction . 6-1
Differential Calculus 6-1
The Derivative of a Function 6-3
Maxima and Minima . 6-11
Integral Calculus 6-15
Indefinite Integrals 6-16
Definite Integrals . 6-16
Summary 6-21
Exercises 6-23
Solutions to Exercises 6-24
Chapter 7
Mathematics of Finance and Economics
Common Terms . 7-1
Interest . 7-6
Sinking Funds 7-23
Annuities . 7-28
Amortization 7-33
Perpetuities 7-36
Valuation of Bonds 7-37
Spreadsheet Financial Functions 7-44
The MATLAB Financial Toolbox 7-58
Comparison of Alternate Proposals . 7-65
Kelvin’s Law 7-68
Summary 7-72
Exercises 7-75
Solutions to Exercises 7-78
Chapter 8
Depreciation, Impairment, and Depletion
Depreciation Defined 8-1
Items that Can Be Depreciated . 8-2
Items that Cannot Be Depreciated . 8-2
Depreciation Rules 8-2
When Depreciation Begins and Ends . 8-3
Methods of Depreciation . 8-3iv Mathematics for Business, Science, and Technology, Second Edition
Orchard Publications
Straight-Line (SL) Depreciation Method 8-4
Sum of the Years Digits (SYD) Method .8-4
Fixed-Declining Balance (FDB) Method .8-6
The 125%, 150%, and 200% General Declining Balance (GDB) Methods 8-8
The Variable Declining Balance (VDB) method .8-9
The Units of Production (UOP) method .8-10
Depreciation Methods for Income Tax Reporting .8-11
The Accelerated Cost Recovery System (ACRS) .8-12
The Modified Accelerated Cost Recovery System (MACRS) 8-12
Section 179 .8-16
Impairments 8-18
Depletion 8-19
Valuation of a Depleting Asset 8-20
Summary .8-25
Exercises .8-27
Solutions to Exercises .8-28
Chapter 9
Introduction to Probability and Statistics
Introduction .9-1
Probability and Random Experiments 9-1
Relative Frequency .9-2
Combinations and Permutations 9-4
Joint and Conditional Probabilities 9-7
Bayes’ Rule 9-10
Summary .9-12
Exercises .9-14
Solutions to Exercises .9-15
Chapter 10
Random Variables
Definition of Random Variables .10-1
Probability Function .10-2
Cumulative Distribution Function .10-2
Probability Density Function 10-9
Two Random Variables 10-11
Statistical Averages 10-12
Summary .10-19
Exercises .10-22
Solutions to Exercises .10-24Mathematics for Business, Science, and Technology, Second Edition v
Orchard Publications
Chapter 11
Common Probability Distributions and Tests
Properties of Binomial Coefficients . 11-1
The Binomial (Bernoulli) Distribution . 11-2
The Uniform Distribution . 11-6
The Exponential Distribution . 11-10
The Normal (Gaussian) Distribution 11-13
Percentiles . 11-32
The Student’s t-Distribution . 11-36
The Chi-Square Distribution 11-41
The F Distribution . 11-44
Chebyshev’s Inequality 11-46
Law of Large Numbers . 11-47
The Poisson Distribution . 11-47
The Multinomial Distribution . 11-52
The Hypergeometric Distribution . 11-53
The Bivariate Normal Distribution . 11-56
The Rayleigh Distribution . 11-57
Other Probability Distributions . 11-59
Sampling Distribution of Means 11-63
Z-Score 11-64
Tests of Hypotheses and Levels of Significance 11-65
The z, t, F, and tests . 11-72
Summary 11-78
Exercises 11-87
Solutions to Exercises 11-89
Chapter 12
Curve Fitting, Regression, and Correlation
Curve Fitting . 12-1
Linear Regression 12-2
Parabolic Regression 12-7
Covariance . 12-10
Correlation Coefficient 12-12
Summary 12-17
Exercises 12-19
Solutions to Exercises 12-21
χ
2vi Mathematics for Business, Science, and Technology, Second Edition
Orchard Publications
Chapter 13
Analysis of Variance (ANOVA)
Introduction .13-1
One-way ANOVA .13-1
Two-way ANOVA .13-8
Two-factor without Replication ANOVA .13-8
Two-factor with Replication ANOVA 13-14
Summary .13-25
Exercises .13-29
Solutions to Exercises .13-31
Appendix A
Introduction to MATLAB®
MATLAB® and Simulink® .A-1
Command Window .A-1
Roots of Polynomials .A-3
Polynomial Construction from Known Roots .A-4
Evaluation of a Polynomial at Specified Values A-6
Rational Polynomials .A-8
Using MATLAB to Make Plots A-10
Subplots .A-19
Multiplication, Division and Exponentiation .A-19
Script and Function Files A-26
Display Formats .A-31
Appendix B
The Gamma and Beta Functions and Distributions
The Gamma Function B-1
The Gamma Distribution .B-15
The Beta Function .B-17
The Beta Distribution .B-20
Appendix C
Introduction to Markov Chains
Stochastic Processes C-1
Stochastic Matrices . C-1
Transition Diagrams C-4
Regular Stochastic Matrices C-5
Some Practical Examples . C-7
x
Symbols and Numerics B column vector A-19
command screen in MATLAB A-1
% (percent) symbol in MATLAB A-2 base 10 logarithm 1-30 Command Window in MATLAB A-1
10-year property 8-14 base 10 number 1-1 commas in MATLAB A-8
125%, 150%, and 200% base of a number 1-21 comment line in MATLAB A-2
Declining Balance 8-8 Bayes’ rule 9-10 common difference 2-19
15-year property 8-15 Bernoulli distribution – see binomial distribution common logarithm 1-30
20-year property 8-15 beta distribution B-20 common prefixes 1-34
25-year property 8-15 beta function B-17 common ratio 2-19
3-year property 8-14 BETADIST Excel function B-20 comparison of alternate proposals 7-65
5-year property 8-14 between groups (in analysis of variance) complementary error function 11-25
7-year property 8-14 degrees of freedom 13-4, 13-19, 13-25 complex conjugate defined A-4
sum of squares 13-4, 13-18, 13-25, 13-28 complex fraction 1-20
A variance 13-4, 13-19, 13-25 complex number A-3
variation 13-1, 13-25 compound interest 7-7
a priori probabilities 9-11 bimodal 2-15 CONCATENATE Excel function 13-22
abs(z) MATLAB function A-24 binary number 1-1 conditional probability 9-7
abscissa 1-37 binomial cone 4-20
absolute value 1-2 distribution 11-2 confidence
absorbing state C-3 coefficients 11-1 interval 11-36
accelerated cost recovery system 8-12 expansion 11-2 levels 11-71
acceleration 6-3 series 11-2 limits 11-71
acquisition costs 8-20 theorem 11-2 CONFIDENCE Excel function 11-71
actual frequencies 11-75 bivariate normal distribution 11-56 congruent 4-18
actual value 8-2 bond 7-1 constant value 1-39
acute angle 5-1 bond rating systems 7-3 continuous random variable 9-2, 10-1
adjoint of a matrix – see matrix book value 7-3, 8-18 conv MATLAB function A-6
algebra 2-1 box MATLAB command A-12 CONVERT Excel function 1-36
algebraic equation 2-2 break-even point 3-3 convertible bond 7-2
alternative depreciation system 8-12 co-ordinates 1-37
alternative hypothesis 11-65 C corporate bond 7-1
amortize function 7-64 CORREL Excel function 12-12
analysis of variance 13-1 calculus defined 6-1 correlation coefficient 11-57
analytic geometry 4-1 capital asset 8-1 COUNT Excel function 13-3, 13-4, 13-9
analytical solution 3-3 capital investment 8-21 coupon bond 7-3
angle defined 5-1 Cartesian coordinate system 1-37, 3-2 COVAR Excel function 12-11
angle(z) MATLAB functionA-24 Cauchy distribution 11-59 covariance 12-10
angle-sum angle-difference relations 5-9 characteristic in logarithms 2-10 Cramer’s rule 3-15, 12-3
annuity 7-5 characteristic function 10-18 CRITBINOM Excel function 11-62
annurate MATLAB function 7-64 Chebyshev’s inequality 11-46 cube 4-18
ANOVA – see analysis of variance CHIDIST Excel function 11-44 cubic equation 2-13
apothem 4-12 CHIINV Excel function 11-44 cubic root 1-29
arbitrary constant of integration 6-15 chi-square (χ2) distribution 11-41 cumulative distribution function 10-2
area of a polygon 4-2 chi-square (χ2) test 11-75 cumulative frequency distribution 10-2
arithmetic mean 2-13 CHITEST Excel function 11-77 cumulative frequency percentages 10-3
arithmetic progression 2-19 circle 4-14 curve fitting 12-1
arithmetic series 2-19 circular cone 4-20 curved regression 12-7
asymptote 4-17 circumference 4-14 cylinder 4-21
AVERAGE Excel function 11-16, 13-9 class life 8-12
average value 2-13 clc MATLAB command A-2 D
average rate of change 6-1 clear MATLAB command A-2
axis MATLAB command A-17 coefficient 2-4 Data Analysis Toolpack in Excel 12-6, 13-6
cofactor 3-11 deceleration 6-9decibels A-13 equation 2-1 frequency response A-12
decimal number 1-1 equilateral triangle 4-6 frustum of cone 4-20
deconv MATLAB functionA-6 equity stripping 7-5 frustum of pyramid 4-19
default in MATLAB Erlang distribution B-15 FTEST Excel function 11-74
color A-15 error F-test 11-74
line A-15 degrees of freedom 13-21 function files in MATLAB A-26
marker A-15 sum of squares 13-20 function-product relations 5-11
definite integral 6-15 variance 13-21 fundamental theorem of
degree defined 5-1 error function 11-25 integral calculus 6-17
degrees of freedom Euclidean geometry 4-1 fundamental trigonometric identities 5-11
between groups 13-4, 13-25 event 9-2, 10-1 FV Excel function 7-46
defined 11-36 exit MATLAB command A-2 fvfix MATLAB function 7-62
for error variation 13-12 EXP Excel function 11-19 fvvar MATLAB function 7-62
for Factor A 13-19 EXP(GAMMALN(n)) Excel function B-5 fzero MATLAB function A-27
for Factor B 13-20 expected frequencies 11-75
for total variation 13-12 expected value 12-10 G
within groups 13-5 exploration costs 8-20
demo in MATLAB A-2 EXPONDIST Excel function 11-12 gamma distribution B-15
dependent variable 6-1 exponent 1-21, 1-30 gamma function B-1
depletion 8-19 exponential distribution 11-10, 11-79 gamma(n) MATLAB function B-3
deposit period 7-23 extrapolation 2-16 GAMMADIST Excel function B-15
depreciation 8-1 GAMMALN Excel function B-5
derivative 6-1 F Gaussian distribution 11-13
descriptive geometry 4-1 Gaussian Elimination Method 3-17
determinant – see matrix F critical value 13-7 General Depreciation System 8-12
development costs 8-20 F distibution 11-44, 13-1 generalized factorial function B-1
diagonals 4-11 F distribution table 13-13 generatrix 4-20
diameter 4-14 F ratio 13-1, 13-5, 13-12, 13-21, 13-26 geometric distribution 11-59
difference 1-3 F values 13-13 geometric progression 2-19
differentiable 6-4 face value 7-2 geometric series 2-19
differential calculus 6-1 Factor A geometry defined 4-1
differentials 6-15 defined 13-14 golden proportion 2-23
differentiation 6-1 degrees of freedom 13-19 golden rectangle 2-24
directrix 4-16 sum of squares 13-18 grand mean 13-9
discrete random variable 10-1 variance 13-19 grand sum 9
discriminant of a quadratic equation 2-12 Factor B graphical solution 3-3
display formats in MATLAB A-31 defined 13-14 grid MATLAB function A-12
dividend 7-38 degrees of freedom 13-20 gtext MATLAB function A-13
dot multiplication operator in MATLAB A-21 sum of squares 13-19
double declining balance 8-8 variance 13-20 H
dummy variable 10-10 factorial 11-1
fair market value 8-19 harmonic progression 2-21
E FDIST Excel function 11-46, 13-6 harmonic series 2-21
figure window A-13 help MATLAB command A-2
eccentricity 4-16, 4-17 FINV Excel function 11-46, 13-6, 13-22 heteroscedastic 11-73
editor window in MATLAB A-2 first derivative 6-1 homoscedastic 11-73
editor/debugger in MATLAB A-1 fixed-declining balance 8-6 hyperbola 4-16
effective interest rate 7-21 flipping 7-5 hypergeometric distribution 11-53
effrr MATLAB function 7-59 fmax in MATLAB A-28 HYPGEOMDIST Excel function 11-55
element-by-element fmin MATLAB function A-27 hypotenuse 4-3
division in MATLAB A-22 foci 4-15
exponentiation in MATLAB A-22 focus 4-15, 4-16 I
multiplication in MATLAB A-19, A-21 format MATLAB command A-31
elements of a matrix – see matrix fplot MATLAB command A-28 identity matrix – see matrix
ellipse 4-15 fractal geometry 4-1 IIR Excel function 7-52
eps MATLAB function A-22 fractional number 1-10 imag(z) MATLAB command A-24
equality 2-2 F-ratio 13-1 impairment 8-18improper integral B-1 squares for straight line 12-2 squares 13-12
increments between points in MATLAB A-14 squares for curve 12-2 square value 10-13
indefinite integral 6-15 squares for parabola 12-2 measure of central tendency 2-13
indenture 7-2 level of significance 11-67 median 2-14, 4-2
independent variable 6-1 limit 6-4 mesh MATLAB command A-17
indeterminate form 6-4 lims = MATLAB function A-28 method of least squares 12-2
infinite sequence 2-18 linear metric system 1-33
infinitesimal 10-5 correlation coefficient 12-13 m-file in MATLAB A-26
inner numbers 1-20 extrapolation 2-16 minor axis 4-15
instantaneous acceleration 6-3 factor A-9 minor of determinant – see matrix
instantaneous velocity 6-2 graph 1-39 minuend 1-3
integer number 1-10, 1-42 interpolation 2-16 minutes defined 5-1
integral calculus 6-1 regression 12-2 MINVERSE Excel function 3-22
integration 6-15 linspace MATLAB command A-14 MIRR Excel function 7-54
interaction 13-14 listed property 8-12 mixed number defined 1-10
defined 13-14 ln (natural logarithm) A-13 MMULT Excel function 3-22
degrees of freedom 13-20 locus 4-14 mode 2-15
plot 13-22 log A-13 modified accelerated
sum of squares 13-20 log(x) MATLAB function A-13 cost recovery system 8-12
variance 13-20 log10(x) MATLAB function A-13 monotonic function 10-4
interest 7-6 log2(x) MATLAB function A-13 mortgage loan 7-4
interior angles 4-10 loglog(x,y) MATLAB command A-13 multinomial distribution 11-52
International System of Units 1-33 lower limit of integration 6-18 municipal bond 7-1
interpolation 2-16 mutually exclusive events 9-3
inverse matrix method of solution 3-21 M
inverse of a matrix – see matrix N
inverse trigonometric functions 5-14 m × n order matrix – see matrix
IPMT Excel function 7-55 main diagonal – see matrix NaN 27, 28
irr MATLAB function 7-58 major axis 4-15 negative binomial distribution 11-59
isosceles triangle 4-5 mantissa of a logarithm 2-10 negative number 1-1
ISPMT Excel function 7-57 Markov chain C-2 NEGBINOMDIST in Excel 11-60
MATLAB – distributions with 11-21 non-Euclidean geometry 4-1
J MATLAB Demos A-2 non-parametric 12-13
matrix, matrices nonresidential real property 8-12, 8-15
joint occurence 9-7 adjoint of 3-18 non-singular 3-19
joint probability conformable for addition 3-7 normal distribution 11-13
defined 9-7 conformable for multiplication 3-8 NORMSDIST Excel function 11-68
density function 10-12 conformable for subtraction 3-7 NORMSINV Excel function 11-69
distribution function 10-11 defined 3-6 NPER Excel function 7-49
junk bond 7-3 determinant of 3-9 NPV Excel function 7-50
diagonal elements 3-7 nth moment about the mean 10-13
K elements of 3-7 null hypothesis 11-65
identity 3-9 number of levels in ANOVA 13-14
Kelvin’s Law 7-68 inverse of
left division in MATLAB 3-24 O
L m × n order matrix 3-7
main diagonal 3-7 obtuse angle 5-1
L’ Hôpital’s rule B-2 minor of determinant 3-12 one-tail
law(s) of multiplication in MATLAB A-19 left test 11-65
cosines 5-12 regular stochastic C-5 right test 11-65
exponents 2-5 square 3-7 test 11-39
logarithms 2-9 stochastic C-1 one-way ANOVA 13-1
of large numbers 11-47 transition C-2 order of precedence 2-1
sines 5-12 zero 3-7 ordinary annuity 7-5
tangents 5-12 Maxwell distribution 11-61 ordinate 1-37, 3-2
LCM Excel function 1-15 mean origin date 7-23
least defined 2-13 overdetermined system 12-3P pyramid 4-19 defined 2-13, 11-36
Pythagorean theorem 4-4 point 10-1
packing 7-5 space 10-1
paired test 11-73 Q sampled mean 11-63
par value 7-2 sampling with replacement 11-54
parabola 4-16 Q function 11-30 script file in MATLAB A-26
parabolic curve 12-1 quadrant 5-3 second defined 5-1
parallel lines 4-11 quadratic second order differential equation 6-20
parallelepiped 4-17 equations 2-11 Section 1245 property 8-13
parallelogram 4-11 factor A-9 Section 1250 property 8-13
Pascal distribution 11-59 curve 12-1 Section 17 property 8-16
Pearson correlation coefficient 12-9, 12-13 quadrilateral 4-11 semicolons in MATLAB A-8
PEARSON Excel function 12-13 quit MATLAB command A-2 semilogx MATLAB command A-13
percentile 11-32 semilogy MATLAB command A-13
PERCENTILE Excel function 11-35 R set of sample points 10-1
perimeter 4-2 similar triangles 4-10
perpendicular 4-2 radian 5-1 simple differential equation 6-15
perpetual bond 7-1 radius 4-14 simple harmonic motion 6-20
perpetuity 7-1 random experiment 9-2 simple interest 7-6
phasor defined 1-39 random variable 9-2, 10-1 sinewave graph 1-40
placed in service 8-12 random variation 13-11 single factor analysis tool 13-6, 13-7
plot MATLAB command A-10, A-13, A-15 RANK Excel function 12-13 single sample point 10-1
PMT Excel function function 7-47 rank correlation coefficient 12-13 singular 3-19
Poisson distribution 11-47 rare event 11-48 sinking fund 7-5
POISSON Excel function 11-51 RATE Excel function 7-48 slope 2-16, 3-2, 6-1
polar MATLAB function A-24 rational polynomials A-8 sphere 4-21
polar form 1-37 Rayleigh distribution 11-57 SQRT Excel function 1-29
polar plot using MATLAB A-25 real numbers 1-2 square 4-11
poly MATLAB function A-4 real(z) MATLAB function A-24 square matrix – see matrix
polyder MATLAB function A-8 reciprocal of a number 1-11 square root 1-28
polygon 4-1 recovery period 8-12 standard deviation 10-14, 12-11
polyval MATLAB function A-6 rectangle 4-11 standard prefixes 1-34
population 9-2, 11-36 rectangular coordinate system 5-3 STANDARDIZE Excel function 11-15
population correlation coefficient 12-12 rectangular form 1-37 standardized form of the
positive number 1-1 rectangular parallelepiped 4-17 normal distribution 11-13
posteriori probabilities 9-11 regression 12-2 state space C-2
power 1-30 regression analysis 12-6 statistical independence 9-9
PPMT Excel function 7-56 regular stochastic matrix – see matrix statistical regularities 9-2
precedence 2-1 relative frequency 9-2 statistically independent 9-9
present value of an ordinary annuity 2-6 research hypothesis 11-65 STDEV Excel function 11-16
principal angle 5-2 residential rental property 8-12, 8-15 step function 10-7
prism 4-18 restoration cost 8-20 Stirling’s asymptotic series B-9
probability rhombus 4-11 stochastic matrix – see matrix
cumulative distribution function 10-2 right angle 5-1 stochastic process C-1
defined 9-1 right circular cylinder 4-21 straight-line depreciation 8-4
density function 10-9 right triangle 4-3 Student’s t-distribution – see t-distribution
differential 10-9 roots MATLAB function A-3 subplot MATLAB function A-19
function 10-2 roots of an equation 2-11 subtrahend 1-3
integral 11-25 ROUND Excel function 11-19 sum
vector C-1 round MATLAB function A-24 identity 2-19
promissory note 7-3 row vector A-3, A-19 of squares for error 13-20
property class 8-12 rth central moment 10-13 of squares for Factor A 13-18
proportion 2-23 rv – see random variable of squares for Factor B 13-19
PV Excel function 7-45 of the years digits 8-4
P-value in ANOVA 13-8 S SUM Excel function 13-9
pvfix MATLAB function 7-60
pvvar MATLAB function 7-60 sampleT for interaction 13-20
variation
t-distribution 11-36 between columns 13-11, 13-16, 13-26
t-test 11-73 between rows 13-9, 13-26
tables of integrals 6-16 due to error 13-11
tangible property 8-13 due to interaction 13-16
TDIST Excel function 11-39 vector 1-39
terminal date 7-24 velocity 6-2
test statistic 11-66 vertex 5-1
text MATLAB command A-13, A-17
title MATLAB command A-12 W
total variation 13-11, 13-12
transition diagram C-4 Wallis’s formulas B-15
transition matrix – see matrix Weibull distribution 11-60
transversal line 4-9 within groups
trapezoid 4-11 degrees of freedom 13-5, 13-25
treasury sum of squares 13-4, 13-25
bill 7-2 variance 13-5, 13-26
bond 7-1 variation 13-1, 13-25
note 7-2
treatments 13-14 X
trendline in Excel 12-4, 12-8
triangle 4-1 x axis defined 1-37
trigonometric identities 5-2 xlabel MATLAB command A-13
trigonometric reduction formulas 5-8 XY (Scatter) in Excel 12-4
trimodal 2-15
TTEST Excel function 11-73 Y
two-dimensional normal distribution 11-57
two-factor y axis defined 1-37
with replication 13-8 y-intercept 3-2
with Replication Analysis Tool 13-6 ylabel MATLAB command A-13
without replication 13-8
without Replication Analysis Tool 13-6 Z
without Replication ANOVA 13-8
two-tail test 11-66 zero coupon bond 7-3
two-way ANOVA 13-8 zero matrix – see matrix
Type z-test 11-72
A investment 8-21 ZTEST Excel function 11-72
B investment 8-20
I error 11-67
II error 11-67
U
undetermined system 12-3
uniform distribution 11-6
units of production 8-10
upper limit of integration 6-18
upper-tail test 11-65
V
variable declining balance 8-9
variance
between groups 13-4, 13-25
defined 10-13, 12-11
for Factor B 13-20

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