This introduces a class of random variables, with the focus on discrete random variables (i.e. on a discrete probability space). This avoids the problem of defining a measure space and measurable functions.
Bases: sage.probability.random_variable.ProbabilitySpace_generic, sage.probability.random_variable.DiscreteRandomVariable
The discrete probability space
The entropy of the probability space.
The set of values of the probability space taking possibly nonzero probability (a subset of the domain).
Bases: sage.probability.random_variable.RandomVariable_generic
A random variable on a discrete probability space.
The correlation of the probability space X = self with Y = other.
The covariance of the discrete random variable X = self with Y = other.
Let be the probability space of
= self,
with probability function
, and
be the
expectation of
. Then the variance of
is:
The expectation of the discrete random variable, namely
, where
= self and
is the probability space of
.
The function defining the random variable.
The standard deviation of the discrete random variable.
Let be the probability space of
= self,
with probability function
, and
be the
expectation of
. Then the standard deviation of
is defined to be
The correlation of the probability space X = self with image of Y = other under map.
The covariance of the probability space X = self with image of Y = other under the given map of the probability space.
Let be the probability space of
= self,
with probability function
, and
be the
expectation of
. Then the variance of
is:
The expectation of the discrete random variable, namely
, where
= self,
is the probability space of
, and
= map.
The standard deviation of the translated discrete random variable
, where
= self and
=
map.
Let be the probability space of
= self,
with probability function
, and
be the
expectation of
. Then the standard deviation of
is defined to be
The variance of the discrete random variable ,
where
= self, and
= map.
Let be the probability space of
= self,
with probability function
, and
be the
expectation of
. Then the variance of
is:
The variance of the discrete random variable.
Let be the probability space of
= self,
with probability function
, and
be the
expectation of
. Then the variance of
is:
Bases: sage.probability.random_variable.RandomVariable_generic
A probability space.
x.__init__(...) initializes x; see help(type(x)) for signature
Bases: sage.structure.parent_base.ParentWithBase
A random variable.
x.__init__(...) initializes x; see help(type(x)) for signature
x.__init__(...) initializes x; see help(type(x)) for signature
x.__init__(...) initializes x; see help(type(x)) for signature
x.__init__(...) initializes x; see help(type(x)) for signature
x.__init__(...) initializes x; see help(type(x)) for signature
x.__init__(...) initializes x; see help(type(x)) for signature
x.__init__(...) initializes x; see help(type(x)) for signature
x.__init__(...) initializes x; see help(type(x)) for signature