KM 1.1 Vrije Universiteit Amsterdam Summary

8/10/2019 KM 1.1 Vrije Universiteit Amsterdam Summary

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Chapter 5: Probability

5.1 Random Experiments

Random experiment: is an observational process whose results cannot be known in

advance. For example, when a customer enters a Shop, will he buy something or not? Howmuch will he spend? Etc.

Sample space(S): The set of all possible outcomes. For example the sample space to

describe rolling a die has six outcomes S={1,2,3,4,5,6}.

5.2 Probability:

Probability of an event os a number that measures the relative likelihood that the event

will occur. It is always a number between 0 1. 0!P(A)!1.

Empirical Probability: Estimated from observed outcome frequency. For

example there is a 2% chance of twins in a randomly chosen birth.

Classical Probability: Known a priori by the bature of the experiment. For

example the is a 50% chance of heads on a coin flip.

Subjective Probability: Based on informed opinion or judgment. For example

The is a 75% chance that England will adopt the euro currency by 2012.Empirical Approach: Sometimes we can collect empirical data through observations or

experiments. We can use the empiricalor relative frequency approach to addign probabilities

by counting frequency of observed outcomes (f) defined in our experimental sample space

and dividing by the number of observations (n). The estimated probability is f/n.

Law of large Numbers:As the number of trials increases, any empirical

probability approaches its theoretical limit.

Classical Approach: Statisticians use the term a priori to refer to the process of

assigning probabilities before we actually observe the eent or try an experiment. When

flipping a coin we do not actually have to perform an experiment because the nature of theprocess allows us to envision the entire sample space.

Subjective Approach: A subjective probability reflects someones informed judgment

about the likelihood of an event.

5.3 Rules of Probability:

Complement of an Event: The complement of an eventAis donetedAand consists ofeveything in the sample space S excepted event A. P(A) + P(A) = 1.

Union of Two event(A "B): The union of two events consists of all the outcomes in

the sample space S that are contained either in ebentAor in eventBor in both.

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KM 1.1 Vrije Universiteit Amsterdam Summary

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