The sample space of a random experiment is the collection of all possible outcomes.
Random variable
A variable whose domain is the sample space, and whose value is somewhat uncertain.
Probability
The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.Probability P(x=a) is the fraction of times x takes value a.
Axioms of probability
Axiom 1: For any event A, P(A) >= 0 Axiom 2: P(true)=1, P(false)=0 Axiom 3: P(A or B) = P(A) + P(B) – P(A and B).
Joint probability
A statistical measure that calculates the likelihood of two events occurring together and at the same point in time. Joint probability is the probability of event Y occurring at the same time that event X occurs.
Marginal probability
The probability of an event irrespective of the outcome of another variable.
Conditional probability
The probability of one event occurring in the presence of a second event.
Bayes rule
Bayes rule describes the probability of an event, based on prior knowledge of conditions that might be related to the event.
Independence
Two events are independent if the occurrence of one does not affect the probability of occurrence of the other.
Conditional Independence
Two random events A and B are conditionally independent given a third event C precisely if the occurrence of A and the occurrence of B are independent events in their conditional probability distribution given C. Note that random variables can be dependent, but conditionally independent.
Expected Value
Calculated as the sum of all possible values each multiplied by the probability of its occurrence.