Bayesian Statistics Midterm || All Questions Answered Correctly.

Bayes' Rule correct answers P(Ai | B) = P(Ai) * P(B | Ai) / Σ P(Aj) * P(B | Aj) Sample Space correct answers The collection of all possible outcomes for an experiment. Event correct answers A collection of outcomes for the experiment, that is, any subset of the sample space. not A correct answers The event A does not occur. A and B correct answers The event both A and B occur. A or B correct answers The event either A or B both occur. Complementation Rule correct answers P(E) = 1 - P(not E) Special Addition Rule correct answers if event A and B are mutually exclusive, then P(A or B) = P(A) +P(B) General Addition Rule correct answers P(A or B) = P(A) + P(B) - P(A and B) Conditional Probability correct answers The probability that event B occurs given that event A occurs. P(B | A) The probability of B given A. Conditional Probability Rule correct answers P(B | A) = P(A and B) / P(A) General Multiplication Rule correct answers P(A and B) = P(A) * P(B | A) Rule of Total Probability correct answers Suppose that events A1, A2, A3, are mutually exclusive and exhaustive; that is, exactly one of the events must occur. Then for any event B: P(B) = Σ P(Aj) * P(B | Aj) exhaustive correct answers Events