STAT211 Chapter Notes - Chapter 4: Collectively Exhaustive Events, Frequentist Probability, Sample Space
26 Jun 2018
School
Department
Course
Professor
Chapter 4.1-4.4
Probability Experiments: An outcome cannot be predicted with certainty in an individual run of
such an experiment.
Frequentist Interpretation (Empirical or relative frequency probability): The probability of an
outcome is the proportion of times that outcome would occur in a very large (infinite) number
of trials.
Bayesian Interpretation: Probability is a measure of how likely an outcome is, given the current
state of knowledge.
Trial: Every toss/roll in an experiment.
Sample Space (S): The set of all possible outcomes of an experiment.
Sample Points: The individual outcomes in a sample space.
Mutually Exclusive: Sample points must be mutually exclusive, no two sample points can occur
on the same trial. Events are mutually exclusive (disjoint events) if they have no outcomes in
common. P(A n B) = 0.
Collectively Exhaustive: Sample points must be collectively exhaustive, the collection of sample
points contains all possible options.
Event: Is a subset of the sample space. An event typically has multiple different outcomes
within it.
Probability of an Event: P(Event) = (# Sample Points in Event)/(Total # Sample Points)
Intersection: The intersection of events A and B is the event that both A and B occur.
P(A n B)
Union: The union of two events is the event that either A or B occurs.
P(A U B) = P(A) + P(B) – P(A n B)
P(A U B) = P(A n Bc) + P(Ac n B) + P(A n B)
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Probability experiments: an outcome cannot be predicted with certainty in an individual run of such an experiment. Frequentist interpretation (empirical or relative frequency probability): the probability of an outcome is the proportion of times that outcome would occur in a very large (infinite) number of trials. Bayesian interpretation: probability is a measure of how likely an outcome is, given the current state of knowledge. Sample space (s): the set of all possible outcomes of an experiment. Sample points: the individual outcomes in a sample space. Mutually exclusive: sample points must be mutually exclusive, no two sample points can occur on the same trial. Events are mutually exclusive (disjoint events) if they have no outcomes in common. Collectively exhaustive: sample points must be collectively exhaustive, the collection of sample points contains all possible options. Event: is a subset of the sample space. An event typically has multiple different outcomes within it.
