&
“Function”
source: Jim Massey's slides of his
crypto coursse
Random variable
from a finite or infinite set,
i.e., discrete or continuous
Distribution and density functions
Distribution function = CDF (Cumulative Distribution Function)
CCDF means Complementary CDF = 1 - CDF
density
Papoulis / Pillai's style:
Continuous and discrete distributions
Special cases
Exponential distribution
Memoryless property of the exponential distribution
Gamma PDF
Erlang PDF
Nth degree Chi-Squared PDF
e.g. resistive
noise
e.g. shadowing in
large-scale fading
e.g. in
small-scale fading
Rice Fading
LoS (line of sight) component
Generalized Gaussian
Source: wiki
Weibull
Source: wiki
Gaussian Mixture Modeling
E.g. in modeling of impulse noise in the Middleton Class A model
Binomial → Poisson
Starting from a binomial distribution, where
Density of Poisson points
If the interval
is sufficiently short
 We sum up two independent random variables. What is the resulting density?
See Example 6-24
Derivation in class!
 Any idea what would happen if two independent random variables would
be multiplied?
 Assume some independent random variables. What does it mean for their probabilities
or densities? In what domain could this be further simplified? What would be the consequence
for the distributions in that domain
Rayleigh distribution in some more detail...
Fading amplitude
is Rayleigh distributed
Home assignment 2:
1.) Assume discrete equal distributed probabilities at -3,-1,+1,+3.
Apply the function
and compute the distribution.
2.) Assume an equal distribution between -3 and 3. What will be the
distribution after applying the same function?
3.) Assume an equal distribution in two dimensions inside a circle of
Radius 1. Determine the one-dimensional marginal.
4.) Assume you like to change a probability plot which had a linearly
spaced abscissa x. Now, you like actually to show the density
dependent on 10 log10(x). Would you have to just rescale the axis,
i.e., do a log plot or are there other measures to think of?