Lecture 1
description
Transcript of Lecture 1
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Lecture 1
Sec 1.1-1.4
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Outline• Define terms with an example
(outcome, sample space, event, an event space)
• Axioms of probability
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Ficticious Experiment• Experiment: flip a coin three times.
Observe the sequence of heads and tails.
– Question: Assuming that the coin is fair, what is the maximum number of heads and tails?
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Ficticious Experiment• Experiment: flip a coin three times. Observe
the sequence of heads and tails.• Results:
– hhh– hht– hth– htt– thh– tht– tth– ttt
outcome
sample space
Definition of an outcome: any possible observation of the experiment
Sample space: a set of all possible outcomes.
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Another Example
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Ficticious Experiment• Procedure: flip a coin three times. Observe
the sequence of heads and tails.• Results:
– hhh– hht– hth– htt– thh– tht– tth– ttt
An event is a set of outcomes with the first flip being a head.
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Exercise• What are the outcomes associated
with each event?
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Event A and event B
Event A and event B are mutually exclusive.
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Event C and Event D
Event C
Event D
Event C and D are not mutually exclusive!
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Exercise• What are the probabilities for event
A, B, C and D?
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Notation• In Set theory, a set is a collection of
things.
x
B is a set.A is a subset of B, i.e. A
A subset can also be empty. A null set, an empty set has no element. The notation of a null is .
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Intersection• The intersection of two sets C and D
is the set of all elements which are contained in both C and D.
Event C
Event D
𝐶∩𝐷
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Union• The union of sets C and D is the set
of all elements that are either in C or in D, or in both.
C
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Mutually Exclusive
𝐴∩𝐵=𝜙
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Quiz• Monitor three consecutive phone calls
going through a telephone switching office. Class each one as a voice call (v) if someone is speaking, or a data (d) if the call is carrying a modem or fax signal. Your observation is a sequence of three letters each letter is either v or d.
• Write down the following events:– First call is a voice call– One or more voice call
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Answer• Write down the following events:– First call is a voice call
A1={vvv,vvd,vdv,vdd}– One or more voice call
A4={vvv,vvd,vdv,dvv,vdd,dvd,ddv}
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Telephone Usage
What is the sample space?What is the probability of the sample space?
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Telephone Usage
What is the probability associated with the long call?
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Telephone Usage
What is the probability associated with the brief callif you know the probability of a long call?