Random Variable

Random variables are used to describe uncertain outcomes in numbers. For example, the number that comes up when a die is rolled is a random variable, with possible values from 1 to 6. Tomorrow's return on a share is also a random variable, since it could take many possible values.

There are two main types. A discrete random variable can take only specific, separate values, such as the number of defaults in a group of loans or the number of customers who visit a shop in a day. A continuous random variable can take any value within a range, such as an interest rate, a share price or the time until a machine breaks down.

The pattern of possible values and their probabilities is called the random variable's probability distribution. From the distribution, analysts can calculate summary measures, such as the expected value, which shows the average outcome, and the variance or standard deviation, which shows how spread out the outcomes are.

In finance, treating returns, losses, interest rates and other uncertain quantities as random variables allows analysts to model risk, price options and insurance, and estimate the chances of different outcomes.