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

Get *Mathematical Formulas for Industrial and Mechanical Engineering* now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.