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Jawaharlal nehru technological university anantapur college of engineering
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Topic:

ComplexVariablesandStatistical
Methods

Definition of probability
• There are two main different definitions of the
concept of probability
• Frequentist
– Probability is the ratio of the number of occurrences of an
event to the total number of experiments, in the limit of very
large number of repeatable experiments.
– Can only be applied to a specific classes of events
(repeatable experiments)
– Meaningless to state: “probability that the lightest SuSy
particle’s mass is less tha 1 TeV”
• Bayesian
– Probability measures someone’s the degree of belief that
something is or will be true: would you bet?
– Can be applied to most of unknown events (past, present,
future):
• “Probability that Velociraptors hunted in groups”
• “Probability that S.S.C Naples will win next championship”
JNTU World
Statistical Methods for Data Analysis
2

Classical probability
“The theory of chance consists in reducing
all the events of the same kind to a certain
number of cases equally possible, that is to
say, to such as we may be equally undecided
about in regard to their existence, and in
determining the number of cases favorable
to the event whose probability is sought.
The ratio of this number to that of all the
cases possible is the measure of this
probability, which is thus simply a fraction
whose numerator is the number of favorable
cases and whose denominator is the number
of all the cases possible.”
Pierre Simon Laplace
(1749-1827)
Pierre-Simon Laplace,
A Philosophical Essay on Probabilities
JNTU World
Statistical Methods for Data Analysis
3

Classical Probability
Number of favorable cases
Probability =
Number of total cases
•
•
Assumes all accessible cases are equally probable
This analysis is rigorously valid on discrete cases only
– Problems in continuous cases ( Bertrand’s paradox)
P = 1/2
P = 1/6
(each dice)
P = 1/4
P = 1/10
JNTU World
Statistical Methods for Data Analysis
4

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