Probability - Basic Terminology

Before we learn about the probability concepts, it is important to know the basic terminology.

Random Variable

A random variable is one of the most important concepts in finance. A random variable is a variable whose value is an outcome of a random phenomenon, for example, this can be viewed as the outcome of throwing a die where the process is fixed but the outcome is not.

Random variables describe key things like asset returns. We then use distribution functions to characterize the random variables.

Outcome

An outcome is a possible result of a probability experiment. For example, a portfolio earning 8% returns is an outcome.

An Event

An event is a single outcome or set of outcomes to which we assign a probability. For example, a portfolio earning 8% returns, or a portfolio earning returns between 6-8%.

Mutually Exclusive Events

These are the events that are mutually exclusive, that is, they cannot happen at the same time. For example, when we throw a die, if one event is to get number 3 and another event is to get number 4 both these events are mutually exclusive; they cannot happen together.

Exhaustive Events

Mutually exhaustive events are those that include all possible outcomes. This means at least one of the events must occur. For example, when we roll a die, the events 1, 2, 3, 4, 5, and 6 are mutually exhaustive, because they include the entire range of possible outcomes. This example is actually mutually exclusive and exhaustive as apart from being all encompassing, no two events can occur together.

Notations

We will use the following notations for probability throughout the reading.

• E denotes an event
• P(E) denotes the probability of an event