Review of probability concepts

Random variables

One definition of a random variable is, "... a variable [whose value] is determined by a chance event ..." This definition is unsatisfying because the dictionary lists "random" as a synonym for "chance." So what is a random event? If you are deeply curious about this, go ask a philosopher. There are lots of good ones around campus. For purposes of making mathematical model of observational error, let's just say that an event is random if we do not know and cannot compute the outcome in advance. The reason why the outcome cannot be predetermined doesn't matter. One kind of random outcome occurs when incomplete information is available about a situation. For example, you might be able to predict the outcome of a coin toss if you had perfect information about the mass distribution of the coin, its initial velocity and angular momentum, the exact atmospheric conditions, the mechanical properties of the surface where it lands, and on and on&hellpi; Or maybe the inherent randomness of the universe works its way into the problem somehow through quantum mechanics. Resolving the exact nature of randomness is not a prerequisite to successfully modeling random events. Whatever the underlying reason, the math works just the same.

With the big questions dispatched, we can easily define a random variable. Here is one: .

The possible outcomes of a random event are given by a probability

Stattrek.com defines a random variable as Random variables play a key role in modeling observational error. A random variable takes