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Zufallsvariable

A Zufallsvariable, also known as a random variable, is a mathematical concept used to describe a value that can take on a set of possible values, each with a certain probability. It is a fundamental concept in probability theory and statistics.

In probability theory, a Zufallsvariable is defined as a function that maps a set of outcomes to

The Zufallsvariable is constructed by specifying the possible outcomes, along with their associated probabilities. For example,

The expected value and variance of a Zufallsvariable are important quantitative measures of its characteristics. The

The use of Zufallsvariables facilitates the analysis and modeling of random events, allowing researchers to quantify

a
set
of
real
numbers.
Each
outcome
is
assigned
a
probability,
and
the
sum
of
the
probabilities
equals
one.
The
Zufallsvariable
is
used
to
model
random
phenomena,
such
as
the
roll
of
a
die
or
the
toss
of
a
coin.
if
the
possible
outcomes
are
the
numbers
1
through
6,
each
with
an
equal
probability
of
1/6,
the
Zufallsvariable
can
be
denoted
as
X
=
{1,
2,
3,
4,
5,
6}
with
assigned
probabilities
P(X
=
1)
=
1/6,
P(X
=
2)
=
1/6,
and
so
on.
expected
value
represents
the
long-run
average
value
of
the
Zufallsvariable,
while
the
variance
measures
the
spread
or
dispersion
of
the
values.
These
concepts
are
crucial
in
various
fields,
including
engineering,
economics,
and
finance.
and
understand
the
underlying
probabilities
and
distributions.