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Lecture_08,_Chap_5,_Sec_1

# Lecture_08,_Chap_5,_Sec_1 - Chapter 5 Probability Sullivan...

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Sullivan – Statistics : Informed Decisions Using Data – 2 nd Edition – Chapter 5 Introduction – Slide 1 of 55 Chapter 5 Probability

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Chapter 5 Preview When we talk about probability , we are talking about a (mathematical) measure of how likely it is for some particular event to happen Probability deals with chance behavior We study outcomes , or results of experiments Each time we conduct an experiment, we may get a different result Probability models the long-term behavior of experiments
Chapter 5 Preview Descriptive statistics, describing and summarizing data, deals with data as it is Probability , modeling data, deals with data as it is predicted to be The combination of the two will let us do our inferential statistics techniques in future chapters

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Probability Learning objectives Understand the rules of probabilities Compute and interpret probabilities using the empirical method Compute and interpret probabilities using the classical method Use simulation to obtain data based on probabilities Understand subjective probabilities 1 2 3 5 4
Probability Probability relates short-term results to long- term results An example: A short-term result: We can obtain 0, 1, 2, or 3 heads when flipping a coin 3 times A long-term result: A “fair” coin would yield heads 1/2 of the time – we would like to use this theory in modeling

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Probability Relation between long-term and theory: The long term proportion of heads after a great many flips is 1/2 This is called the Law of Large Numbers – as the number of repetitions of an experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of that outcome Helpful Hint: Look over p. 252 of your textbook for more information about the Law of Large Numbers.
Probability Some definitions An experiment is a repeatable process where the results are uncertain An results are uncertain An outcome is one specific possible result The set of all possible outcomes is the sample space Example Experiment … roll a fair 6 sided die One of the outcomes … roll a “4” The sample space … roll a “1” or “2” or “3” or “4” or “5” or “6”

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Probability More definitions An event is a collection of possible outcomes … we will use capital letters such as E for events Outcomes are also sometimes called simple events … we will use lower case letters such as e for outcomes / simple events An will use capital letters such as Outcomes are also sometimes called … we will use lower case letters such as for outcomes / simple events Example (continued) One of the events … E = {roll an even number}
Probability If E is an event, then we write P ( E ) as the probability of the event E happening Probability Rules: The probability of any event must be greater than or equal to 0 and less than or equal to 1

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