sta291 5c

57 %
43 %
Information about sta291 5c
Entertainment

Published on October 29, 2007

Author: funnyside

Source: authorstream.com

Introduction to Probability:  Introduction to Probability Experiments, Outcomes, Events and Sample Spaces What is probability? Basic Rules of Probability Probabilities of Compound Events Experiments, Outcomes, Events and Sample Spaces :  Experiments, Outcomes, Events and Sample Spaces Experiment: An experiment is any activity from which results are obtained. A random experiment is one in which the outcomes, or results, cannot be predicted with certainty. Examples: Flip a coin Flip a coin 3 times Roll a die Draw a SRS of size 50 from a population Trial: A physical action , the result of which cannot be predetermined Basic Outcomes and Sample Spaces:  Basic Outcomes and Sample Spaces Basic Outcome (o): A possible outcome of the experiment Sample Space: The set of all possible outcomes of an experiment Example: A company has offices in six cities, San Diego, Los Angeles, San Francisco, Denver, Paris, and London. A new employee will be randomly assigned to work in on of these offices. Outcomes: Sample Space: Slide4:  Example #2: A random sample of size two is to be selected from the list of six cities, San Diego, Los Angeles, San Francisco, Denver, Paris, and London. Outcomes: Sample Space: Events and Venn Diagrams:  Events and Venn Diagrams Events: Collections of basic outcomes from the sample space. We say that an event occurs if any one of the basic outcomes in the event occurs. Example #1 (cont.): Let B be the event that the city selected is in the US Let A be the event that the city selected is in California Venn Diagram: Graphical representation of sample space and events Slide6:  Example #2: A random sample of size two is to be selected from the list of six cities, San Diego, Los Angeles, San Francisco, Denver, Paris, and London. Let E be the event that both cities selected are in the US E= Sample Space and Venn Diagram: Assigning Probabilities to Events:  Assigning Probabilities to Events Probability of an event P(E): “Chance” that an event will occur Must lie between 0 and 1 “0” implies that the event will not occur “1” implies that the event will occur Types of Probability: Objective Relative Frequency Approach Equally-likely Approach Subjective Slide8:  Relative Frequency Approach: Relative frequency of an event occurring in an infinitely large number of trials Equally-likely Approach: If an experiment must result in n equally likely outcomes, then each possible outcome must have probability 1/n of occurring. Examples: Roll a fair die Select a SRS of size 2 from a population Subjective Probability: A number between 0 and 1 that reflects a person’s degree of belief that an event will occur Example: Predictions for rain Odds:  Odds Example: If the odds of Came Home winning the Derby are 9:2, what is the subjective probability that he will win? Probabilities of Events:  Probabilities of Events Let A be the event A = {o1, o2, …, ok}, where o1, o2, …, ok are k different outcomes. Then Problem 5.3.4: The number on a license plate is any digit between 0 and 9. What is the probability that the first digit is a 3? What is the probability that the first digit is less than 4? Probabilities of Compound Events:  Law of Complements: “If A is an event, then the complement of A, denoted by , represents the event composed of all basic outcomes in S that do not belong to A.” Additive Law of Probability: Probabilities of Compound Events A S Law of Complements:  “If A is an event, then the complement of A, denoted by , represents the event composed of all basic outcomes in S that do not belong to A.” Law of Complements Unions and Intersections of Two Events:  Unions of Two Events “If A and B are events, then the union of A and B, denoted by AB, represents the event composed of all basic outcomes in A or B.” Intersections of Two Events “If A and B are events, then the intersection of A and B, denoted by AB, represents the event composed of all basic outcomes in A and B.” Unions and Intersections of Two Events Additive Law of Probability:  Additive Law of Probability Using Additive Law of Probability:  Using Additive Law of Probability Example: At State U, all first-year students must take chemistry and math. Suppose 15% fail chemistry, 12% fail math, and 5% fail both. Suppose a first-year student is selected at random. What is the probability that student selected failed at least one of the courses? Mutually Exclusive Events:  Mutually Exclusive Events Mutually Exclusive Events: Events that have no basic outcomes in common, or equivalently, their intersection is the empty set. S Multiplication Rule and Independent Events:  Multiplication Rule and Independent Events Multiplication Rule for Independent Events: Let A and B be two independent events, then Examples: Flip a coin twice. What is the probability of observing two heads? Flip a coin twice. What is the probability of getting a head and then a tail? A tail and then a head? One head? Three computers are ordered. If the probability of getting a “working” computer is .7, what is the probability that all three are “working” ?

Add a comment

Related presentations

Related pages

Introduction to Probability powerpoint download

Introduction to Probability powerpoint. Last Update: 2012-06-18 07:19:23. Details; View Online; Comments; Tags; File Name : sta291 5c.ppt. Size : n/a ...
Read more

Sample Spaces | Many PPT

http://web.as.uky.edu/statistics/users/astro11/sta291_5c.ppt. Preview. Download. Filesize: 5094 KB | format : .PPT .
Read more

⚡Presentation "Regression Wisdom Getting to Know Your ...

Regression Wisdom Getting to Know Your Scatterplot and Residuals.
Read more

Quick View http://east.instructor.ilrn.com/ilrn/bca/instr ...

Quick View http://east.instructor.ilrn.com/ilrn/bca/instr/test-printing/1154691255... ... 5 c 6 b 7 8 9 10 b 11 a 12 a 13 b 14 b 15 d 16 17 18 ANSWER KEY ...
Read more

Chapter 4 - Chapte r4: Describing Data: Displaying and ...

View Notes - Chapter 4 from STATS 3 at Texas Southern. Chapte r4: Describing Data: Displaying and Exploring Data Chapter Opener GOALS When you have
Read more

3. Consider a document-term matrix, where f ij is the ...

Consider a document-term matrix, where f ij is the ... S t a t s 4 1 5 C l u s t e r A n a l y s i s ... STA291 Summer2010 Lecture1 DustinLueker ...
Read more

Copyright © 2010, 2007, 2004 Pearson Education, Inc ...

Copyright © 2010, 2007, 2004 Pearson Education, Inc. *Chapter 29 Multiple Regression.
Read more

Probability - Scribd - Read books, audiobooks, and more

Probability - Ebook download as PDF File (.pdf), Text File (.txt) or read book online. Probability
Read more

www.scribd.com

Preface; Basic Operations on Sets; 1 Basic Definitions; 2 Set Operations; Counting and Combinatorics; 3 The Fundamental Principle of Counting; 4 ...
Read more

1 - Documents

... “STA200andadding”,12min- utestodealwith“STA200andswitching”,8minutestodealwith“STA291 ... = C(5, 0)(0.4) 0 (0.6) 5 +C(5, 1)(0.4) 1 (0 ...
Read more