NOTATION, SYMBOLS AND ABBREVIATIONS
This document provides a brief overview of the notational conventions, symbols the abbreviations used throughout the course. It is expected that the students are familiar
with all terms listed in this document at the very beginning of the course.
Sets
N
Z
R
Zn
Rn
The
The
The
The
The
set
set
set
set
set
natural numbers {1, 2, 3, . . .}
integer numbers {. . . , −2, −1, 0, 1, 2, . . .}
real numbers
n-dimensional vectors with integer entries
n-dimensional vectors with real-valued entries
of
of
of
of
of
Abbreviations
pmf
pdf
cdf
i.i.d.
Abbreviation
Abbreviation
Abbreviation
Abbreviation
for
for
for
for
probability mass function (discrete random variables)
probability density function (continuous random variables)
cumulative distribution function (all random variables)
independent and identically distributed
Random variables (definitions)
X is a discrete RV
P (X = x)
X is a continuous RV
P (X ∈ A)
the
the
the
the
range of X is countable (finite or infinite)
probability that X equals the outcome x
cdf FX (x) is a continuous function (range of X uncountable)
probability that an outcome of X belongs to the set A
Functions
A function f which maps from the general set V to the general set W is written as
f : V → W . For example, with the cosine function we would write cos : R → [−1, 1].
List of symbols etc.
δ(k)
δ(t)
1[·]
N (µ, σ 2 )
U(a, b)
F{·}
E[X]
Var[Y ]
Cov[X, Y ]
E[X n ]
∼
∀
×
∗
:=
Kronecker delta function (k being a discrete variable)
The Dirac delta (t being a continuous variable)
Indicator function, e.g. 1[k = 0] = δ(k)
Gaussian distribution with mean µ ∈ R and variance σ 2 > 0
Uniform distribution with pdf f (·) = 1[a ≤ · ≤ b](b − a)−1 where a < b
Fourier transform
Expected value of the random variable X
Variance of the random variable Y
Co-variance between X and Y
The n’th moment of X
Means distributed as, e.g. X ∼ N (µ, σ 2 )
Means for all
Cartesian product, e.g. R2 = R × R
Convolution
h
2 i
Left hand side defined as right hand side, e.g. Var[Y ] := E Y − E[Y ]