Editing Random variable (section)

===Mixed type===

A '''mixed random variable''' is a random variable whose [[cumulative distribution function]] is neither [[discrete random variable|discrete]] nor [[Continuous function|everywhere-continuous]].<ref name=":0" /> It can be realized as a mixture of a discrete random variable and a continuous random variable; in which case the {{Abbr|CDF|cumulative distribution function}} will be the weighted average of the CDFs of the component variables.<ref name=":0" />

An example of a random variable of mixed type would be based on an experiment where a coin is flipped and the spinner is spun only if the result of the coin toss is heads. If the result is tails, '''''X''''' = −1; otherwise '''''X''''' = the value of the spinner as in the preceding example. There is a probability of {{frac|1|2}} that this random variable will have the value −1. Other ranges of values would have half the probabilities of the last example.

Most generally, every probability distribution on the real line is a mixture of discrete part, singular part, and an absolutely continuous part; see {{Section link|Lebesgue's decomposition theorem|Refinement}}. The discrete part is concentrated on a countable set, but this set may be dense (like the set of all rational numbers).