Variables- What are they?
statistical probability, a random or stochastic variable
is something that changes continuously because of
randomness and chance. When compared to other
mathematical variables, a random one will not have a
fixed, single value; rather, the random variable has the
possibility to become different values that are each
associated with a different probability.
The possible value of a random variable can represent
many possible outcomes of an experiment or the possible
outcomes of an experiment that has uncertain results
such as imprecise measurements or incomplete
information. Random variables can also represent an
objectively random process or a subjective random
process that results from not enough information of a
quantity. The meaning of a particular probability that
is assigned to a random variable is not necessarily part
of the actual probability itself. Instead, it can be
related to various philosophical arguments over the
understanding of probability. Regardless, the
mathematics is still going to be the same regardless of
what interpretation is used.
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Random variables are categorized into two sets: discrete
or continuous. A discrete variable is only a specified
list of exact values, and a continuous variable is a
value that is in an interval or collection of intervals.
The mathematical function that is responsible is
explaining the possible outcomes of a random variable
and its probability is defined as the probability
distribution. The results of a random variable of
choosing their values according to the probability
distribution is known as random variates.
In probability theory, there is a formal treatment of
mathematical random variables. In this context, a random
variable is defined on a sample space where the outputs
are only numerical values.
An example of a random variable can include a person’s
height. In a mathematical sense, the random value is
understood as a function that maps the particular person
to their height. The random value is also associated
with the probability distribution that allows the
calculation of the particular probability that the
height of a person is a non-pathological subset of
different values. Examples include that the height is
between 170 and 180 cm, or that the probability that the
height is either less than 140 or more than 190 cm.
In this particular example, the sample space is
suppressed since it is difficult to mathematically
describe, and the possible values of the variables are
then treated as the actual sample space. But when two
different random variables are being measured on the
same outcome, such as the height of a person, it is very
easy to track the overall relationship if there is an
acknowledgment that the height comes from the same
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