Statistics and Quantitative Analysis U4320 - PowerPoint PPT Presentation

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Statistics and Quantitative Analysis U4320

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The relative frequency with which events occur when repeated many times. ... Example: What is the probability of exactly two heads AND having the first toss be heads? ... – PowerPoint PPT presentation

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Title: Statistics and Quantitative Analysis U4320


1
Statistics and Quantitative Analysis U4320
  • Segment 3 Probability
  • Prof. Sharyn OHalloran

2
Review Descriptive Statistics
3
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4
Statistics
5
Example Employment
6
How raw data maps into a frequency table
7
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8
Probability Theory
  • Simple Probability
  • The relative frequency with which events occur
    when repeated many times.
  •  Property As N gets large

9
Example Toss a coin 3 times
  • Outcome Space
  • Simple probability- The frequency of A divided
    by the total number of outcomes.

10
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

11
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.

12
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

13
Probability Tables
14
Independence
  • Definition The occurrence of one event does
    not affect the probability of the other.
  •  
  • P(AB) P(A)
  • Example
  •  
  • 20 of the students play football, 50 play
    basketball, and 15 play both. How can we put
    this into a table?

15
  • 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?
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