Statistics and Quantitative Analysis U4320

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Statistics and Quantitative Analysis U4320

• Segment 3 Probability
• Prof. Sharyn OHalloran

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Review Descriptive Statistics
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Statistics
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Example Employment
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How raw data maps into a frequency table
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Probability Theory

• Simple Probability
• The relative frequency with which events occur
  when repeated many times.
•  Property As N gets large

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Example Toss a coin 3 times

• Outcome Space
• Simple probability- The frequency of A divided
  by the total number of outcomes.

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Compound Events

• A and B
• Example What is the probability of exactly two
  heads AND having the first toss be heads?
• Definition The relative frequency of the
  events that meet both criteria

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A or B

•  Example What is the probability of getting
  either exactly 2 heads or no heads at all?
•   Definition The probability of A or B is the
  relative frequency of the events that meet either
  criteria.

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Conditional Probability (A given B)

• Example What is the probability that the first
  toss is a head given that there are exactly two
  heads?
•  Denote P(1st H/2H)
•  Definition

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Probability Tables
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Independence

• Definition The occurrence of one event does
  not affect the probability of the other.
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• P(AB) P(A)
• Example
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• 20 of the students play football, 50 play
  basketball, and 15 play both. How can we put
  this into a table?

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• What's the probability that a student selected at
  random will
• a) Play neither sport?
• b) Play football or basketball?
• c) Are playing basketball and football
  independent?