Bnal chpt4

Know the purpose of Bayes Theorem, and when you would use it.

-used to revise previously calculated probabilities based on new information.

Complement

All events that are not part of event A. e.g., All days from 2018 that are not in January.

Simple Event

An event described by a single characteristic. e.g., A day in January from all days in 2018.

Joint Event

An event described by two or more characteristics. e.g. A day in January that is also a Wednesday from all days in 2018.

Event

Each Possible Outcome Of A Variable

Statistical Independence

Events A and B are independent when the probability of one event is not affected by the fact that the other event has occurred

Mutually Exclusive

Events that cannot occur simultaneously. Example: Randomly choosing a day from 2018 A = day in January; B = day in February Events A and B are mutually exclusive.

Use the addition rule to determine a compound probability for both general use and for mutually exclusive events.

General rule - P(A or B)= P(A) + P(B) - P(A and B) -If mutually exclusive then P(A and B)=0 , so P(A or B)= P(A) + P (B)

Use the multiplication rule to determine a joint probability for both dependent and independent sets of variables

Independent- P(A and B)= P(A)P(B)

Joint ("and")

Joint Probability refers to the probability of an occurrence of two or more events (joint event). ex. P(Plan to Purchase and Purchase). ex. P(No Plan and Purchase). P(A and B)= # of outcomes satisfying A and B/ total # of outcomes

Collectively Exhaustive

One of the events must occur. The set of events covers the entire sample space. Example: Randomly choose a day from 2018. A = Weekday; B = Weekend; C = January; D = Spring; Events A, B, C and D are collectively exhaustive (but not mutually exclusive - a weekday can be in January or in Spring). Events A and B are collectively exhaustive and also mutually exclusive.

Marginal (Simple)

P(Planned) = P(Yes and Yes) + P(Yes and No) = 200 / 1000 + 50 / 1000 = 250 / 1000 P(A)= # of outcomes satisfying A/ total # of outcomes

Compound or Conditional

P(Purchased | Planned) = P(Purchased and Planned) / P(Planned) = (200 / 1000) / (250 / 1000) = 200 / 250 P(A/B)=P(A and B)/ P(B) OR P(B/A)=P(A and B)/P(A)

Sample Space

The Collection Of All Possible Outcomes Of A Variable Ex. 1.2.3.4.5.6 of a dice

Probability

the numerical value representing the chance, likelihood, or possibility that a certain event will occur (always between 0 and 1).

Conditional Probability

the probability of one event, given that another event has occurred