SOCECOL 13 Chapter Notes - Chapter 14: Frequentist Probability, Cumulative Distribution Function
20 May 2018
School
Department
Course
Professor
Jessica Mangold
SE13 Statistics
Professor Wong
May 20, 2018
Chapter 14: Understanding Probability & Long-Term Expectations
14.1 Probability
- two distinct interpretations of the term probability
- can quantify the chances exactly (winning the lottery)
- base assessment on personal beliefs (chances of buying home in future)
- clear conceptual difference
14.2 The Relative-Frequency Interpretation
- Introduction
- relative-frequency interpretation = applies to probability situations in which
we can envision observing results over + over again
- ex. flipping a coin over + over
- relative frequency over long run in which coin lands heads up
- The Idea of Long-Run Relative Frequency
- probability = the proportion of time an outcome occurs over the long run
- aka relative frequency of that outcome
- emphasis on ‘in the long run’ -> cannot assess probability of outcome by
observing only few times
- can be misled if make judgements too soon
- Determining the Probability of an Outcome
- Method 1: Make an Assumption about the Physical World
- make an assumption based off of physical world to determine probability
of an outcome
- ex. based on the way coins are manufactured -> can conclude that
probability of flipped coin showing heads up is ½
- does not mean that outcome will happen once every two flips
- Method 2: Observe the Relative Frequency
- observe relative frequency over many repetitions of the situation
- ex. relative frequency of male births in given city in a year
- can get accurate figure through this method
- sometimes relative-frequency probabilities reported on basis of sample
surveys
- should include margin of error
- useful in making daily decisions -> look for better performance in long
run
14.3 The Personal-Probability Interpretation
- Introduction
- relative frequency interpretation limited to repeatable conditions
- uncertainty is a characteristic of most events
- can have unique situations that are not likely to be repeated
- have to make decisions based on how future will evolve
- Defining Personal Probability
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Document Summary
Can quantify the chances exactly (winning the lottery) Base assessment on personal beliefs (chances of buying home in future) Relative-frequency interpretation = applies to probability situations in which we can envision observing results over + over again. Ex. flipping a coin over + over. Relative frequency over long run in which coin lands heads up. Probability = the proportion of time an outcome occurs over the long run. Emphasis on in the long run" -> cannot assess probability of outcome by observing only few times. Two distinct interpretations of the term probability. Make an assumption based off of physical world to determine probability of an outcome. Ex. based on the way coins are manufactured -> can conclude that probability of flipped coin showing heads up is . Does not mean that outcome will happen once every two flips. Method 1: make an assumption about the physical world. Observe relative frequency over many repetitions of the situation.
