2- Information and Uncertainty Flashcards
What is an outcome space (Ω)?
The set of all possible individual outcomes Ω={A1,…An}
What is the OR axiom?
If A and B are mutually exclusive, the probability of A or B is the sum of the two P(A∪B)=P(A)+P(B)
What is the AND rule?
If A and B are independent, the probability of A and B is the product of the two P(A∩B)=P(A)xP(B)
What is the conditional probability formula?
P(A|B) = P(A∩B)/P(B)
What is the General AND rule?
P(A∩B) = P(A|B)xP(B)
What are 2 ways of proving independence?
- P(A|B)=P(A)
- P(A∩B)=P(A)xP(B)
What is the rule of total probability?
P(A)=[P(A|B)xP(B)]+[P(A|¬B)xP(¬B)]
What is Bayes’ rule?
P(A|B) = [P(B|A)xP(A)]/P(B)
What is Prior probability in Bayesian updating?
The probability that a hypothesis is true P(H) before evidence E is revealed
What is Posterior probability in Bayesian updating?
The probability that a hypothesis H is true given evidence E is revealed P(H|E)
What is the Bayesian updating formula for posterior probability?
P(H|E) = [P(E|H)xP(H)]/[P(E|H)xP(H)+P(E|¬H)xP(¬H)]
What is the Gambler’s fallacy?
Belief, that a departure from the average behaviour of some (random) system will be corrected in the short term
What is the conjunction fallacy?
The false belief that 2 events occurring is more likely than one of those events occurring
What is the disjunction fallacy?
Underestimating the probability of a disjunction e.g. feminist bank clerk
What is the base-rate?
The fraction of some population that has some characteristic of interest
