1 Introduction to Probability

Wednesday, January 04, 2012

11:29 AM

1. A simple classification of real world phenomena

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:

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

Implication to daily life.

(Jan 05)

1.  Random events

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

• 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

 Probability (Prob.) A quantitative measurement on how likely a random event will occur under repeated trials.

1.  The relative frequency of an event.

Let

Let

Eg.

Flip a coin.

0.5

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

Definition 2

 Probability

1.  Frequency interpretation of prob.

"0.2" has no meaning.

Eg.

Eg.

1.  Subjective prob.

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?

1.  Classic definition of prob.

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

Created by Tim Pei with Microsoft OneNote 2010
One place for all your notes and information