1.3 Linear Algebra Symbol
1.4 Probability and Statistics Symbols
Symbols How to Read It How to Use It Examples
P(A) probability function probability of event AP(A) 5 0.5
P(A - B) probability of events
intersection
probability that of
events A and B
P(A - B) 5 0.5
P(A , B) probability of events
union
probability that of
events A or B
P(A , B) 5 0.5
P(AjB) conditional probability
function
probability of event A
given event B
occurred
P(AjB) 5 0.3
f(x) probability density
function (pdf)
P(a # x # b) 5
Ð
f(x)dx
F(x) cumulative distribution
function (cdf)
F(x) 5
P(X # x)
μ population mean mean of population
values
μ 5 10
E(X) expectation value expected value of
random variable X
E(X) 5 10
E(XjY) conditional expectation expected value of
random variable X
given Y
E(XjY 5 2) 5 5
var(X) variance variance of random
variable X
var(X) 5 4
(Continued)
Symbols How to Read It How to Use It Examples
dot scalar product a b
3 cross vector product a 3 b
A B tensor product tensor product of A and BAB
hx; yi inner product
[ ] brackets matrix of numbers
( ) parentheses matrix of numbers
jAj determinant determinant of matrix A
det(A) determinant determinant of matrix A
jjxjj double vertical bars norm
A
T
transpose matrix transpose (A
T
)
ij
5 ( A)
ji
A
†
Hermitian matrix matrix conjugate transpose ( A
†
)
ij
5 (A)
ji
A
Hermitian matrix matrix conjugate transpose ( A
)
ij
5 (A)
ji
A
21
inverse matrix AA
21
5 I
rank(A) matrix rank rank of matrix A rank(A) 5 3
dim(U) dimension dimension of matrix A rank(U) 5 3
4 Mathematical Formulas for Industrial and Mechanical Engineering
(Continued)
Symbols How to Read It How to Use It Examples
σ
2
variance variance of population
values
σ
2
5 4
std(X) standard deviation standard deviation of
random variable X
std(X) 5 2
σ
X
standard deviation standard deviation value
of random variable X
σ
X
5 2
~
x median middle value of random
variable x
~
x 5 5
cov(X,Y) covariance covariance of random
variables X and Y
cov(X,Y) 5 4
corr(X,Y) correlation correlation of random
variables X and Y
corr(X,Y) 5 3
ρ
X,Y
correlation correlation of random
variables X and Y
ρ
X,Y
5 3
Mod mode value that occurs most
frequently in
population
MR mid range MR 5 (x
max
1 x
min
)/2
Md sample median half the population is
below this value
Q
1
lower/first quartile 25% of population are
below this value
Q
2
median/second quartile 50% of population are
below this
value 5 median of
samples
Q
3
upper/third quartile 75% of population are
below this value
X sample mean average/arithmetic mean x 5 (2 1 5 1 9)/
3 5 5.333
s
2
sample variance population samples
variance estimator
s
2
5 4
S sample standard
deviation
population samples
standard deviation
estimator
s 5 2
z
x
standard score z
x
5 ( x 2 x)/s
x
XB distribution of X distribution of random
variable X
XBN(0,3)
N(μ,σ
2
) normal distribution Gaussian distribution XBN(0,3)
U(a,b) uniform distribution equal probability in
range a, b
XBU(0,3)
exp(λ) exponential distribution f(x) 5 λe
2λx
, x $ 0
(Continued)
5Symbols and Special Numbers
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