Prob Stat I

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Prob Stat I

• Notes to Parrots
• R. Sinn
• August 25, 2005

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Chapter 1 Vocabulary

• Sample (Observations) vs. Population
• Descriptive Statistics
• Inferential Statistics
• Mean, median and standard deviation
• Simple Random Sampling (SRS)
• Biased vs. Unbiased Sampling
• Sample Mean vs. Population Mean
• Sample Standard Deviation vs. Population Standard
  Deviation
• Trimmed Mean
• Exploratory Data Analysis
• Stem-and-Leaf Plot, Frequency Tables, Histograms
• Probability Distributions
• Normal Distribution (Bell Curve)

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Chapter 1 Tasks

• Find mean, median and standard deviation
• Determine sample vs. population in an experiment

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Chapter 2 Vocabulary

• Sample Space
• Elements Outcomes (Sets)
• Set complements, unions, intersections and
  cardinality
• Mutually exclusive or independent events
  (disjoint sets)
• Combinations Permutations
• Basic Probability Formulas
• P(A) n(A) / n(S)
• P(not A) 1 P(A)
• P(either A or B) P(A U B ) ??
• P(both A and B) P(A n B) ??
• P(B given A occurred) P(B A) ??
• 10P6 vs. 10C6 vs. 6!
• Sampling With Replacement vs. Sampling Without
  Replacement

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Chapter 2 Tasks

• Learn to organize and detail every outcome of a
  given probability sample space
• Use knowledge of basic probabilities to analyze
  probability experiments
• Use knowledge of factorials, combinations and
  permutations to count large numbers quickly
• Begin to connect binomial theorem (PT) to
  probability investigations

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Organizing the Sample Space

• Four main ways
• Ordered List
• Used For Very small sample spaces ( n(S) lt 10 )
• Probability Tree
• Used For Multinomial or Binomial experiments
  with 5 or fewer repetitions.
• Matrix or Table
• Used For Two independent Multinomial
  experiments
• Venn Diagram
• Used For Dependent events or experiments

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Examples Organizing the Sample Space

• How many outcomes are possible from flipping a
  coin two times?
• How many outcomes are possible from flipping a
  coin three times?
• How many outcomes are possible from rolling a
  pair of dice and summing?
• What is the probability of drawing a straight
  flush in poker?

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Permutations, Combinations and Factorials

• Permutations
• Ordered
• Combinations
• Unordered
• Factorial
• Total possible permutations given n things

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Examples Combinations, Permutations Factorials

• Twenty runners compete in a cross-country meet.
• How many different Top 10s are possible?
• How many different Wins-Place-Shows are
  possible?
• How many different total orders of finish are
  possible?

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Poker Examples

• What is the probability, if 3 cards are drawn at
  random from a standard deck of cards, of all 3 of
  them being spades?
• What is the probability, if 3 cards are drawn at
  random from a standard deck of cards, of all 3 of
  them being 3s?
• How many possible poker hands are there?
• How many possible flushes are there?

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Urn Examples

• An urn contains 5 red balls, 3 green balls and 7
  yellow balls. Two are drawn at random without
  replacement. Find the probability of drawing
• both red
• 1 green and 1 yellow
• no red
• Same questions, with replacement.