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You probably first remember learning about variables in your elementary algebra class. You probably remember solving for x and y in equations such as

Maybe you then moved on to geometry where you were asked to find the degrees of an angle given partial information about other angles and line segments. For example, suppose you were asked to find x and y in the figure below.

These variables can be determined mathematically.

A random variable is a variable whose value cannot be determined mathematically, but rather it needs to be observed. Prior to observation, the value of that variable is unknown and therefore random. Some examples of random variables are

• the outcome of a basketball game (Bernoulli)
• the number of heads in ten tosses of a coin (Binomial)
• the number of cars crossing a particular intersection in a 10-minute period (Poisson)
• the average height of a group of 50 people (Gaussian)

Note that before the event occurs, you do not know what the outcome will be. The names in parentheses are the typical probability distributions used to model their associated examples. Statisticians typically denote a random variable by an upper case Roman letter, e.g.

This notation says that Y, the outcome of the basketball game, has a Bernoulli distribution with parameter p where p is the probability of the home team winning.

There are many more of these distributions: geometric, negative binomial, beta, chi-squared, gamma, log-normal, etc. Each random variable is associated with a probability distribution that determines the probability of realizing different values for the random variable. In subsequent posts, I will outline the different probability distributions and give examples of where each might be used.