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Statistics and Quantitative Analysis U4320

Statistics and Quantitative Analysis U4320. Segment 3 : Probability Prof. Sharyn O’Halloran. Review Descriptive Statistics. Statistics. Example: Employment. How raw data maps into a frequency table. Probability Theory. Simple Probability

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Statistics and Quantitative Analysis U4320

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  1. Statistics and Quantitative Analysis U4320 Segment 3: Probability Prof. Sharyn O’Halloran

  2. Review Descriptive Statistics

  3. Statistics

  4. Example: Employment

  5. How raw data maps into a frequency table

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

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

  8. 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

  9. 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.

  10. 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:

  11. Probability Tables

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

  13. 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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