Introduction to Probability Part 1-Probability And Statistics-Lecture Slides, Slides of Probability and Statistics

Download Introduction to Probability Part 1-Probability And Statistics-Lecture Slides and more Slides Probability and Statistics in PDF only on Docsity!

Slide 1

Introduction to Probability

Slide 2

Introduction to Probability

Topics

 Experiments and the Sample Space

 Assigning Probabilities to

Experimental Outcomes

 Events and Their Probability

 Some Basic Relationships

of Probability

 Bayes’ Theorem

Slide 4

Experiments and Sample Space

Experiment Experimental Outcomes

Toss a coin Head, Tail

Select a part for inspection Defective, Nondefective

Conduct a sales call Purchase, No Purchase

Roll a die 1, 2, 3, 4, 5, 6

Play a football game Win, Lose, Tie

Each of the experimental outcomes is called a sample

point. All of the potential outcomes is known as the

sample space and are usually shown within { }.

Slide 5

Requirements for Probabilities

 The probability values assigned to each experiment outcome (sample point) must be between 0 and 1. If we let Ei indicate the ith^ experimental outcome and P(Ei) indicate the probability of this experimental outcome, we must have: 0 <= P( Ei ) <= 1

 The sum of all the experimental outcome probabilities must be 1. For example, if a sample space has k experimental outcomes, we must have P( E 1 ) + P( E 2 ) + … + P( Ek ) = 1

Slide 7

Events and Their Probabilities

An experiment is any process that generates

well-defined outcomes.

The sample space for an experiment is the set of

all sample points.

An experimental outcome is also called a sample

point.

An event is a collection of particular sample points.

Slide 8

Classical Method

If an experiment has n possible outcomes, this method

would assign a probability of 1/ n to each outcome.

Experiment: Rolling a die Sample Space: S = {1, 2, 3, 4, 5, 6} Probabilities: Each sample point has a 1/6 chance of occurring

Example

Slide 10

Each probability assignment is given by

dividing the frequency (number of polishers) by

the total frequency (total number of days).

Relative Frequency Method

Probability

Number of Polishers Rented

Number of Days 0 1 2 3 4