Probability - Basic Terminology
Before we learn about the probability concepts, it is important to know the basic terminology.
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.
An outcome is a possible result of a probability experiment. For example, a portfolio earning 8% returns is an outcome.
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.
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.
We will use the following notations for probability throughout the reading.
- E denotes an event
- P(E) denotes the probability of an event
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- Probability - Basic Terminology
- Two Defining Properties of Probability
- Empirical, Subjective and Priori Probability
- State the Probability of an Event as Odds
- Unconditional and Conditional Probabilities
- Multiplication, Addition and Total Probability Rules
- Joint Probability of Two Events
- Probability of Atleast One of the Events Occuring
- Dependent Vs. Independent Events in Probability
- Joint Probability of a Number of Independent Events
- Unconditional Probability Using Total Probability Rule
- Expected Value of Investments
- Calculating Variance and Standard Deviation of Stock Returns
- Conditional Expected Values
- Calculating Covariance and Correlation
- Expected Value of a Portfolio
- Variance and Standard Deviation of a Portfolio
- Bayes’ Theorem
- Multiplication Rule of Counting
- Permutation and Combination Formula