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Elementary Statistics

by: Morgan Walker

Elementary Statistics Stat 2013

Morgan Walker
OK State
GPA 3.2

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About this Document

Chapter 4- Probability
Elementary Statistics
Robert Adam Molnar
Class Notes
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This 2 page Class Notes was uploaded by Morgan Walker on Sunday February 7, 2016. The Class Notes belongs to Stat 2013 at Oklahoma State University taught by Robert Adam Molnar in Winter 2016. Since its upload, it has received 92 views. For similar materials see Elementary Statistics in Statistics at Oklahoma State University.


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Date Created: 02/07/16
Chapter 4 Probability Probability is a way to assign numerical measurement to chance, 3 ways to do this  Theoretical “classical”- computed through mathematical definitions  Empirical- frequency proportion of the time that events of the same type will occur in the long run  Subjective- assigned estimate of chance considering data, experience and personal belief In classical all possible outcomes are equally likely  Very bad, very unlikely only works for cards and dice Probability experiment- chance process that’ll lead to 1 out of 2 or more defined results Trial- a process of observation or measurement Outcome- result of a trial Sample space (s)- set of all possible outcomes Event-set of one or more outcomes inside a sample space, denoted with a capital letter Empty space- set with no elements, denoted with a Ø Probability Rules 1. The probability of any event (E) is a real number between and including 0 and 1 a. 0 ≤ P(E)≤ 1 2. The sum of the probabilities of all outcomes in a sample space is 1 a. P(S)=1 3. If an event cant occur the probability is 0 4. If an event is certain to occur its probability is 1 Complement- the set of outcomes in the sample space Ex: heads is compliment of tails and vice versa Balanced or fair implement- equal probability assigned for each outcome Mutually Exclusive 2 events are mutually exclusive if they have no outcomes in common Both events cannot occur in the same trial Mutually Exclusive events are labeled A and B P(A&B)=0 General Addition Rule For any two events A&B in the sample space (s) P(A&B)= P(A)+P(B)- P(A&B) When A and B are mutually exclusive the last term becomes zero Venn Diagrams Graphical tool to examine events Conditional Probability Conditional Probability of event B given event A, is the probability that event B occurs computed with knowledge that event A happened in this trial Given that A occurs, B has a different probability than if A didn’t occur Denote given information on the right side of bar B|A “B given A” Independent Events If knowledge about A doesn’t change the probability for event B P(B|A)= P(B) Testing Independence P(A&B)=P(A) X P(B|A) = P(B) X P(A|B) (general) P(B|A)=P(A&B)/P(A) If and only if both are independent then use this formula P(A&B)=P(A) X P(B)


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