1 Introduction to Probability

Wednesday, January 04, 2012

11:29 AM

- A simple classification of real world phenomena
- Statistics
- (The science of data)
- Actuarial Science
- Calculating risk
- Computer Science
- OCR
- Engineering
- Random events
- 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).
- The relative frequency of an event.
- Frequency interpretation of prob.
- Subjective prob.
- Classic definition of prob.

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)

Created by Tim Pei with Microsoft OneNote 2010

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