What is a random variable? Choose the correct answer below. A. A random variable is a numerical measure, having either a finite or countable number of values, of the outcome of a probability experiment. B. A random variable is a numerical measure of the outcome of a probability experiment. C. A random variable is a numerical measure, having values that can be plotted on a line in an uninterrupted fashion, of the outcome of a probability experiment.

A random variable can be said to be a numerical measure of the outcome of a probability experiment. It is unpredictable although the range of possible outcomes and the probability of each outcome may be known. For example, it is impossible to know in advance the outcome of a toss of a coin, but it must be either heads or tails, each with probability one-half. The number of heads in250 tosses is another random variable, which can take any value between zero and 250. You are very unlikely to get 250 heads from tossing a fair coin!

Random variables are often designated by letters. They are often used in econometric or regression analysis to determine statistical relationships among one another.

Types of Random Variables

A random variable can be either discrete or continuous.

Discrete random variables: this takes on a countable number of distinct values. Consider an experiment where a coin is tossed two times. If X represents the number of times that the coin comes up heads, then X is a discrete random variable that can only have the values 0, 1, 2 (from no heads in two successive coin tosses to all heads). No other value is possible for X.

Continuous random variables: this represents any value within a specified range or interval and can take on an infinite number of possible values. For instance, an experiment that involves measuring the amount of rainfall in a city over a year.