AP STATISTICS LESSON 6 - 1

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AP STATISTICSLESSON 6 - 1

• THE IDEA OF PROBABILITY

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ESSENTIAL QUESTION How is probability used in
Statistics?

• Objectives
• To develop a working understanding of
  Probability.
• To understand what is meant by Random, and what
  its characteristics are in the long run.

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Introduction

• Probability is a branch of mathematics that
  describes the pattern of chance outcomes.
• The reasoning of statistical inference rests
  on asking, How often would this method give a
  correct answer if I used it many, many times?

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The Idea of Probability

• Probability begins with the observed fact that
  some phenomena are random that is , the
  relative frequencies of their outcomes seem to
  settle down to fixed values in the long run.
• The big idea is this chance behavior is
  unpredictable in the short run but has a regular
  and predictable pattern in the long run.
• The tossing of a coin can not be predicted in
  just a few flips, but there is a regular pattern
  in the results, a pattern that emerges clearly
  only after many repetitions.

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Example 6.1

• Page 331
• COIN TOSSING
• For the first few tosses the proportion of
  heads fluctuates quite a bit, but settles down as
  we make more and more tosses.

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Randomness and Probability

• Randomness in statistics is not a synonym for
  haphazard but a description of a kind of order
  that emerges only in the long run.
• The idea of probability is empirical. That
  is, it is based on observation rather than
  theorizing.

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Randomness and Probability(definitions)

• We call a phenomenon random if individual
  outcomes are uncertain but there is nonetheless a
  regular distribution of outcomes in a large
  number of repetitions.
• The probability of any outcome of a random
  phenomenon is the proportion of times the outcome
  would occur in a very long series of repetitions.
  That is, probability is long term relative
  frequency.

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Thinking about Randomness

• That some things are random is an observed fact
  about the world.
• Independent The outcome of one trial must not
  influence the outcome of any other.