What is a random variable?
An uncertain value determined by chance.
What is an outcome?
The realization of a random variable.
What is an event? What are mutually exclusive events? Exhaustive events?
- An event is a set of one or more outcomes
- Two events that cannot occur simultaneously are deemed mutually exclusive
- A set of events that includes ALL possible outcomes is considered “exhaustive”
What are the two properties of probabilities?
- The sum of probabilities for all mutually exclusive events is 1
- The probability of any events cannot be greater than 1 or less than 0.
What does a priori probability measure?
- Measures predetermined probabilities based on well defined imputs.
- Most often used within the deduction method of calculating probability.
- Ex: consider how the price of a share can change. Its price can increase, decrease or remain the same. Therefore, according to a priori probability, we can assume that there is a 1-in-3, or 33%, chance of one of the outcomes occurring (all else remaining equal).
What is empirical probability?
- Measures probability from observations or experiments
- In order for a theory to be proved or disproved, empirical evidence must be collected. An empirical study will be performed using actual market data.
- Ex: Many empirical studies have been conducted on the capital asset pricing model (CAPM), and the results are slightly mixed.
What is subjective probability?
- An informed guess
- Subjective probabilities differ from person to person. Because the probability is subjective, it contains a high degree of personal bias.
- Ex: Asking Eagles fans the chances of Philly winning the Super Bowl. While there is no absolute mathematical proof behind the answer to the example, fans might still reply in actual percentage terms, such as the Eagles having a 25% chance of winning.
What is unconditional probability?
- AKA marginal probability
- The probability of an event occuring
- An unconditional probability is the independent chance that a single outcome results from a sample of possible outcomes.
What is conditional probability?
- P(A|B)
- The probability of an event “A” occuring given that event “B” has occured.
- Calculated by multiplying the probability of the preceding event by the updated probability of the succeeding event.
What is the multiplication rule of probability?
- P(AB) = P(A|B) x P(B)
- Used to determine the joint probability of two events
What is the addition rule of probability?
- P(A or B) = P(A) + P(B) - P(AB)
- Used to determine that at least one of two events will occur
What is the total probability rule?
- Used to determine the unconditional probability of an event.
- P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) +…+ P(A|Bn)P(Bn)
- B1, B2, BN are mutually exclusive and exhaustive
What is the joint probability of two events?
- The probability that both events will occur
- P(AB) = P(A|B) x P(B)
What is the probability of two independent events?
- P(A|B) = P(A), so that..
- P(AB) = P(A) x P(B)
What is the formula for the probability of at least one of two events occuring?
- P(A or B) = P(A) + P(B) - P(AB)
What is a tree diagram?
- Shows the probabilities of two events and the conditional probabilities of two subsequent events.
What is covariance?
- Measures the extent to which two random variables tend to be above and below their respective means for each joint realization.
- A measure of the degree to which returns on two risky assets move in tandem.
- Positive covariance means that asset returns move together.
- Negative covariance means returns move inversely.
- Ex: Possessing financial assets that have a high covariance with each other will not provide very much diversification.
What is correlation?
- A standardized measure of association between two random variables
- Ranges in value from -1 to +1
- In the world of finance, a statistical measure of how two securities move in relation to each other. Correlations are used in advanced portfolio management.
What is Baye’s Formula for updating an event based on the occurence of event “O”?
Can be used to rate the risk of lending money to potential borrowers.
