QTA 1 Flashcards
What is the Counting Principle?
A method to determine the number of ways to select objects from a set.
What does the Combination Rule calculate?
The number of ways of selecting r different objects out of n different objects.
What is a Random Experiment?
An experiment whose result is unknown.
Define Random Variable.
A variable whose value is unknown.
What is a Sample Space?
The set of all possible outcomes of an experiment.
What is an Event in probability?
A subset of the sample space, representing one or several outcomes.
What is the Event Space?
The set of all combinations of outcomes to which probabilities can be assigned.
What does a probability measure?
The likelihood that some event occurs.
What is the frequentist interpretation of probability?
The frequency with which an event would occur if independent experiments were run.
What are Mutually Exclusive Events?
Events that cannot happen together.
What is the probability of two mutually exclusive events A and B occurring?
P(A ∩ B) = 0.
What are the three fundamental principles of probability?
- Pr(A) ≥ 0
- Pr(Ω) = 1
- For mutually exclusive events: Pr(A1 ∪ A2) = Pr(A1) + Pr(A2)
What are Exhaustive Events?
Events that form the sample space, ensuring at least one will occur.
Define Independent Events.
Two events where the occurrence of one does not affect the probability of the other.
What is Unconditional Probability?
The probability of an event irrespective of any other events.
What is Conditional Probability?
The probability of an event given that another event has occurred.
How is Joint Probability defined?
The probability that two events will occur together.
What is Conditional Independence?
Events A and B are conditionally independent if P(A ∩ B|C) = P(A|C) P(B|C).
What is the Theorem of Total Probability?
Unconditional probability can be calculated from conditional probabilities of mutually exclusive and exhaustive events.
What is Bayes’ Theorem?
A formula to change beliefs in light of new evidence: P(A|B) = P(B|A) × P(A) / P(B).
What is the significance of Bayesian analysis?
Heavily used in finance and risk management.
What is Bayesian analysis commonly used for?
Finance and risk management
Bayesian analysis provides a framework for updating probabilities as more information becomes available.
What is Bayes’ Theorem primarily used for?
Calculating conditional probabilities
Bayes’ Theorem allows for the revision of probabilities based on new evidence.
