Chapter 2, Section 2 Probability and Inference

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Chapter 2, Section 2Probability and Inference
? John J Currano, 07/01/2007
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• Experiment A process by which an observation is
  made
• Deterministicsame conditions ? same result
• Deposit 1000 in CD paying 5 simple interest
• Stochastic or Randomoutcome varies even if
  conditions are the same
• Toss 10 coins and count the number of heads that
  show
• Drop a brick from the roof and measure time it
  takes to hit the ground

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• Stochastic or Random Experiment
• Toss a coin and observe the face that shows
• Outcome varies from trial to trial
• Sample Space (set of all possible outcomes)
  isheads, tails
• We cannot say in advance which outcome will
  occur, but is there anything we can say?
• How likely is it that the outcome is heads?
  tails?
• How can we measure likelihood?

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• Stochastic or Random Experiment
• Toss a coin n times and count the number of
  times that a head shows
• The relative frequency of the outcome heads in
  these n tosses is
• Conceptualize tossing 10, 100, 1000, 10000,
  times
• Observe what happens to the relative frequency of
  heads does it approach a limit?
• Intuitively, the probability of heads is the
  long-range relative frequency of heads

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• Stochastic or Random Experiment
• Toss 10 coins and count the number of heads that
  show
• Outcome varies from trial to trial
• Sample Space (set of all possible outcomes)
  is0, 1, 2, , 10
• We cannot say in advance which outcome will
  occur, but is there anything we can say?
• Are some outcomes more likely to occur than
  others?
• If so, which ones?
• How much more likely is one of them than another?
• How can we measure likelihood?

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• Stochastic or Random ExperimentToss 10 coins and
  count the number of heads
• Perform n trials (do the experiment n times)
• Compute the relative frequencies of the events of
  obtaining 0 heads, 1 head, 2 heads, , 10 heads,
  respectively, on the n trials
• Virtual Laboratories in Statistics (Kyle
  Siegrist, University of Requires Mozilla Firefox
  Alabama, Huntsville)
• Rossman/Chance Applet

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• Stochastic or Random ExperimentToss 10 coins and
  count the number of heads
• Perform n trials (do the experiment n times)
• Compute the relative frequencies of the events of
  obtaining 0 heads, 1 head, 2 heads, , 10 heads,
  respectively, on the n trials
• By comparing the long-range relative
  frequencies of these events, we can make a start
  towards answering some of the earlier questions
• Are some outcomes more likely to occur than
  others?
• If so, which ones?
• How much more likely is one of them than another?
• How can we measure likelihood?