Download Randomness and Probability

BUSA 3321 - Probability
Probability – the bedrock of
randomness
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Definitions
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Random experiment – observing the close
of the NYSE and the Nasdaq
Sample space = {NYSE+Nasdaq+,
NYSE+Nasdaq-, NYSE-Nasdaq+, NYSENasdaq-}
Simple event = {NYSE+Nasdaq+}
Event = the NYSE is up
Approaches to probability
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Classic – equal likelihood
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Relative frequency – historic data, relative
frequency distributions
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Dice, cards, inventory control, polls, audits –
(random samples)
Actuarial tables
Race track odds
Subjective
Which for the NYSE and the Nasdaq?
Probabilities of Combinations
of Events
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Union of sets – “or”
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The NYSE is up or Nasdaq is up
Intersection of sets – “and”
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Joint events
The NYSE is up and the Nasdaq is up
Conditional Probability
P (A|B) = P(A and B)/P(B)
A and B are independent if
P(A|B) = P(A)
Which also means that
P(B|A) = P(B)
Probability the Nasdaq is up given that
the NYSE is up.
Rules of Probability
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Complement
Addition
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General
Special
Multiplication
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General
Special
Rules:
Complement: P(A complement) = 1 – P(A)
Addition: P(A or B) = P(A) + P(B) – P(A and B)
P(A or B) = P(A) + P(B) if A and B are
mutually exclusive
Multiplication:P(A and B) = P(A|B) * P(B)
P(B|A) * P(A)
P(A and B) = P(A) * P(B) if A and B are
independent
Probability table
Nasdaq + NasdaqNYSE +
x
NYSE 0.6
0.4
P(Nasdaq+|NYSE+) = .5
x/.7 = .5
0.7
0.3
Probability table
Nasdaq + NasdaqNYSE +
0.35
0.35
NYSE 0.25
0.05
0.6
0.4
P(Nasdaq+|NYSE+) = .5
x/.7 = .5
0.7
0.3
Diagnostics and False Positives
Test +
Test Disease
True positive False negtive
No disease False positive True negative
P(Test+|Disease) = Sensitivity
P(Test -| No disease) = Specificity
Summary:
The approach to assigning probabilities must be
chosen:
any probability must be between 0 and 1, inclusive
the probability of the sample space is 1
The language of probability is the language of
set theory.
Learn the complement, addition and
multiplication rules.
Tables help in determining joint and marginal
probabilities.