1 Introduction to Probability

Wednesday, January 04, 2012

11:29 AM

    1. A simple classification of real world phenomena


    Important Deterministic


    Outcomes can be predicted precisely from an initial set of conditions.

    "If you give me a set of conditions, I can provide you with the outcome."


    Eg) finding the 3rd angle of a triangle.



    Important Random (Stochastic)


    Outcomes cannot be predicted precisely from an initial set of conditions.


    Eg) Rolling a dice



    Many applications:

    • Statistics
      • (The science of data)
    • Actuarial Science
      • Calculating risk
    • Computer Science
      • OCR
    • Engineering


    Implication to daily life.


    (Jan 05)


    1. Important Random events

    Possible outcomes of a random trial/process/experiment



    Randomly take a hand of 13 cards from a standard deck of 52 (13 Diamonds, 13 Hearts, 13 Spades, 13 Clubs)


    A = "The hand consists of all 13 diamonds"

    B = "The hand has at least 1 diamond"



    • Run the trial only once, any event will either occur or not occur, but not both!
    • Repeat the trial many times (under the same set of conditions).

    B appears more often than A!

    B is more likely to occur!


    Definition 1




    A quantitative measurement on how likely a random event will occur under repeated trials.


    1. Important The relative frequency of an event.











    Flip a coin.










    Definition of prob. based on the stability of the relative frequency:


    Definition 2








    1. Important Frequency interpretation of prob.



    "0.2" has no meaning.












    1. Important Subjective prob.

    Arbitrary measure of confidence.



    What is the probability that a terrorist crashed a plane on the twin towers on 9/11?

    What is the probability that the moon landing happened?


    1. Important Classic definition of prob.


    (A special case of Definition 2; Chapters 2 & 3)


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