A random variable is a function that assigns a unique numerical value to every possible event having an outcome dependent on chance. The random variable will typically be different for each new event, such as a new toss of a coin. The term was first coined in 1949, and Merriam-Webster defines it as follows:
- a variable that is itself a function of the result of a statistical experiment in which each outcome has a definite probability of occurrence - called also variate
There are discrete and continuous random variables. An example of a discrete random variable is the number of heads observed in the ten tosses of a coin. This random variable can only have the values 0, 1, 2, ... or 10. An example of a continuous random variable is the mileage on your car until it breaks down. It can have any positive value.
The terminology "random variable" has been criticized as being neither "random" nor "variable". A random variable really consists of a sampling from a certain probability distribution. It is not purely "random" because it is limited by the predefined probability distribution (e.g., "heads" or "tails" in the case of a coin toss, with a likelihood of each determined by the likelihood of each side appearing); it is not a "variable" because it is a sample value from that distribution.
- Merriam-Webster's Collegiate Dictionary 10th Edition (1994).