13 Facts About Random variable

Random variable is a mathematical formalization of a quantity or object which depends on random events.

Sometimes a random variable is taken to be automatically valued in the real numbers, with more general random quantities instead being called random elements.

Random variable is a measurable function from a set of possible outcomes to a measurable space.

Any random variable can be described by its cumulative distribution function, which describes the probability that the random variable will be less than or equal to a certain value.

Mathematically, the random variable is interpreted as a function which maps the person to the person's height.

Random variable can be used to describe the process of rolling dice and the possible outcomes.

Formally, a continuous random variable is a random variable whose cumulative distribution function is continuous everywhere.

An example of a continuous random variable would be one based on a spinner that can choose a horizontal direction.

In general, the probability of a set for a given continuous random variable can be calculated by integrating the density over the given set.

Mixed random variable is a random variable whose cumulative distribution function is neither discrete nor everywhere-continuous.

In more intuitive terms, a member of is a possible outcome, a member of is a measurable subset of possible outcomes, the function gives the probability of each such measurable subset, represents the set of values that the random variable can take, and a member of is a "well-behaved" subset of .

The random variable is then a function from any outcome to a quantity, such that the outcomes leading to any useful subset of quantities for the random variable have a well-defined probability.

Probability distribution of a random variable is often characterised by a small number of parameters, which have a practical interpretation.