1 Introduction to Probability
Wednesday, January 04, 2012
11:29 AM
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.
Random (Stochastic)
Outcomes cannot be predicted precisely from an initial set of conditions.
Eg) Rolling a dice
Many applications:
Implication to daily life.
(Jan 05)
Possible outcomes of a random trial/process/experiment
Eg
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"
Observations
B appears more often than A!
B is more likely to occur!
Definition 1
Probability (Prob.) |
A quantitative measurement on how likely a random event will occur under repeated trials. |
Let
Let
Eg.
Flip a coin.
0.5
Definition of prob. based on the stability of the relative frequency:
Definition 2
Probability |
"0.2" has no meaning.
Eg.
Eg.
Arbitrary measure of confidence.
Eg.
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?
(A special case of Definition 2; Chapters 2 & 3)
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