Understanding Randomness

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Chapter 11

• Understanding Randomness

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What does it mean to be random?

• We use the word random fairly often.
• The numbers drawn in the lottery are random.
• We hope the casino slot machines are random.
• What prize we get in a Cracker Jack box is
  random.
• We view things that are random as being fair.
• But what does it really mean???
• Write down what you think it means.

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Pick a card, any card

• What card will you get when you pick a card at
  random?
• You know the possibilities
• You dont know what card youll get, until you
  look at the card!
• Random event We know what outcomes could happen,
  but not which particular value will occur.
• We cannot predict the outcome in advance.
• We will also see patterns (a regular
  distribution) emerge, in the long run.

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Random Babies

• Website applet
• Random Babies
• Can you predict an individual outcome ( of
  correct matches)?
• Is there a pattern emerging in the long run
  (large number of trials)?

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Equally likely?

• If an event is random, does that necessarily mean
  that the outcomes are equally likely?
• Some things are Coin flips, die rolls
• Some things arent Winning the lottery
• Can you think of others?
• What about this spinner?

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Biased Coin?

• I have a coin that someone gave me.
• They said it was biased towards usually landing
  on heads.
• What does that mean?
• How should I test it?
• What would convince you it was biased?
• Key question What would happen if we did this
  many times??

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Exploring Randomness

• How can we explore this idea of what would be
  unusual?
• Experience random events flip lots of coins
• Flip coin 10 times. Record H/Ts.
• Streaks?
• Simulate random events
• Modeling the event
• Fast

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Setting up a simulation

• Identify component to be repeated
• Flipping of coin
• Set up model for outcome.
• Random number table
• Digits 0-9 equally likely.
• Heads Digits 0-4, Tails digits 5-9
• How will you simulate the trial?
• Look at each random number, indicates H or T
• What are we interested in?
• Number of heads in 20 flips
• Run several trials
• Lets try it!

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Basketball

• Marc has an 80 free throw success rate.
• How many shots can he make before he misses?
• What is the component?
• Taking a shot
• How should we model it?
• 0-7 good shot 8-9 missed shot
• Whats the trial?
• Look at random numbers until we get a miss
• Whats the response variable?
• Number of shots made before misses.
• What statistic can we estimate?
• Mean number of shots made before missing

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ActivStats Tool Randomness

• Go to Chapter 11 in ActivStats
• Click on first icon in Chapter 11.
• Is it random?
• Click on tool
• Run 300 trials (25 at a time)
• What proportion of red did you get?
• Did everyone get the same proportion?
• Were Red and Blue outcomes equally likely?

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Its a model, though

• Double Chocolate Sugar Bombs Get a special free
  Matchbox car in each box! Collect all 5!
• How many boxes do I need to buy before I get the
  green car that Marc is whining for?
• Say I run a simulation, it suggests that Ill
  have to buy 10 boxes.
• Is that what will actually happen when I go to
  the store?

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Another simulation

• Marcs class has 15 boys, 12 girls.
• Theyre selecting 3 kids at random to pick the
  books to read for the week.
• How likely it is well get 3 boys?
• Can simulate to estimate this.
• Component?
• Student chosen
• How to model?
• 00-14 boy, 15-26 girl
• Skip numbers above 26.
• Trial?
• Select 3 students (2 digits at a time, ignore
  repeated numbers)
• Response variable?
• Were all 3 students male?
• Statistic? Percentage of trials that produced all
  males.

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Rectangles

• We can use simulations to help us estimate a
  population parameter.
• In-class activity