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31/03/2008 21:57:00
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Statistics Prelim 2
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Chapter 14
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A phenomenon consists of trials.
Each trial has an outcome.
Outcomes combine to
make events.
The combination of all possible outcomes is the sample space
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As you collect more data, the outcomes becomes smaller and smaller fraction of
accumulated experiences, so in the long fun the probability settles out
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Law of Large Numbers
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If we assume that events are independent, and the outcome of one trial does
not affect the outcome of the others, the LLN saws that as the number of trials
increases, the longrun relative frequency of repeated events gets closer and
closer to a single number
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Called probability of an event
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Because the definition is based on repeatedly observing the event’s outcome,
this definition of probability is often called empirical probability.
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Deals with the long run not the short run
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No Law of Averages that promises shortterm compensation for recent deviations
from expected behavior.
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When outcomes are equally likely, it is just 1 divided by the number of possible
outcomes
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P(A) = # outcomes in A / # of possible outcomes
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We use the language of probability in everyday speech to express a degree of
uncertainty without basing it on long run relative frequencies or mathematical
models, this is known as personal probability
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Three rules for working with probability – Make a picture (3x)
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Rules of Probability
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1.) A probability is a number between 0 and 1
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2.) Probability assignment rule – the set of all possible outcomes of a trial
must have the probability of 1, P(S) = 1
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3.) Complement Rule – the probability of an event occurring is 1 – the
probability that it doesn’t occur, P(A) = 1 – P(Ac)
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4.) Addition Rule – for two disjoint events A and B, the probability that one or
the other occurs is the sum of the probability of the two event
P(A or B) = P(A) + P(B), provided the events are disjoint
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Disjoint: no outcomes in common, mutually exclusive
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5.) Multiplication Rule: For two independent events A and B, the probability
that both A and B occur is the product of the possibilities of the two events
P(A and B) = P(A) x P(B), provided that the two events are
independent
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Independent: knowing whether one event occurs does not alter the probability
that another even occurs
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The phrase “at least” is often a tipoff to think about the complement.
Something that
happens at least once is the complements of something not happening
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Independence Assumption:
It’s unlikely that the choice made by one respondent
affected the choice on another
WHAT CAN GO WRONG
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Beware of probabilities that don’t add up to 1
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Don’t add probabilities of events of they are not disjoint
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Don’t multiply probabilities of events of they are not independent.
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This note was uploaded on 05/09/2008 for the course ILRST 2100 taught by Professor Vellemanp during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 VELLEMANP

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