Chapter6_STAT1100.ppt", filename="Chapter6_STAT1100.ppt", filename="Chapter6_STA

# Chapter6_STAT1100.ppt", filename="Chapter6_STAT1100.ppt", filename="Chapter6_STA

This preview shows pages 1–14. Sign up to view the full content.

Probability Statistics for Management and Economics Chapter 6

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Objectives Assigning Probability to Events Joint, Marginal, and Conditional Probability Probability Rules and Trees Bayes’ Law Identifying the Correct Method
Probability Chance There’s a 99% chance that we’ll discuss Probability in today’s class Critical component of statistical inference Used for decision making

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Random Experiment A random experiment is an action or process that leads to one of several possible outcomes. For example: Experiment Outcomes Flip a coin Heads, Tails Exam Marks Numbers: 0, 1, 2, . .., 100 Assembly Time t > 0 seconds Course Grades F, D, C, B, A, A+
Probabilities List the outcomes of a random experiment… This list must be exhaustive , i.e. ALL possible outcomes included. Die roll {1,2,3,4,5} Die roll {1,2,3,4,5,6} The list must be mutually exclusive , i.e. no two outcomes can occur at the same time: Die roll {odd number or even number} Die roll{ number less than 4 or even number}

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Sample Space A list of exhaustive and mutually exclusive outcomes is called a sample space and is denoted by S. The outcomes are denoted by O 1 , O 2 , …, O k Using notation from set theory, we can represent the sample space and its outcomes as: S = {O 1 , O 2 , …, O k }
Requirements of Probabilities Given a sample space S = {O 1 , O 2 , …, O k }, the probabilities assigned to the outcome must satisfy these requirements: (1) The probability of any outcome is between 0 and 1 i.e. 0 ≤ P(O i ) ≤ 1 for each i , and (1) The sum of the probabilities of all the outcomes equals 1 ) + P(O 2 ) + … + P(O k ) = 1 P(O i ) represents the probability of outcome i

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Approaches to Assigning Probabilities Classical approach : make certain assumptions (such as equally likely, independence) about situation. Relative frequency : assigning probabilities based on experimentation or historical data. Subjective approach : Assigning probabilities based on judgment or prior experience
Classical Approach If an experiment has n possible outcomes, this method would assign a probability of 1/ n to each outcome. Experiment: Rolling a die Sample Space: S = {1, 2, 3, 4, 5, 6} Probabilities: Each sample point has a 1/6 chance of occurring.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Classical Approach Experiment: Rolling dice Sample Space: S = {2, 3, …, 12} Probability Examples: P(10) = 3/36 P(6) = 5/36 P(2) = 1/36 1 2 3 4 5 6 1 2 3 4 5 6 7 5 6 7 8 3 4 5 6 7 8 9 8 9 10 9 10 11 6 7 8 9 10 11 12 What are the underlying,  unstated assumptions??
Relative Frequency Approach Bits & Bytes Computer Shop tracks the number of desktop computer systems it sells over a month (30 days): For example, 10 days out of 30 From this we can construct the probabilities of an event (i.e. the # of desktop sold on a given day)… Desktops Sold # of Days 0 1 1 2 2 10 3 12 4 5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Relative Frequency Approach Desktops Sold # of Days Desktops Sold 0 1 1/30 = .03 1 2 2/30 = .07 2 10 10/30 = .33 3 12 12/30 = .40 4 5 5/30 = .17  ∑ = 1.00 “There is a 40% chance Bits & Bytes will sell 3 desktops on any given day”
Subjective Approach “In the subjective approach we define

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 06/25/2008 for the course BUSSPP MCE taught by Professor Atkins during the Spring '08 term at Pittsburgh.

### Page1 / 42

Chapter6_STAT1100.ppt", filename="Chapter6_STAT1100.ppt", filename="Chapter6_STA

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online