An Introduction to Probability
Theory
Santosh Appathurai
*
The true logic of this world is the calculus of probabilities.
Pierre–Simon de Laplace
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An introduction to this
Introduction
Very broadly, one could say that probability is the study of averages of phenomena. The basic
notion here is that of a random experiment – one whose outcome is not known
apriori
(Mathspeak
for beforehand), but some reasonable predictions can be made on the lines of what it (the outcome)
would likely be. The classic examples here would include tossing a coin, rolling a die or picking out
a card at random from a well-shuFed pack of cards. This was because in its initial days, probability
theory was mainly used to analyze games of chance. To be slightly more precise, it all
probably
started in ±rance in the mid-17th century, when a nobleman who was rather fond of gambling wrote
to two of his compatriots, who happened to be rather fond of numbers (for an elaborate story, see
Section 5). ±ollowing its hedonistic beginnings, probability underwent much of the rigor, and soon
acquired the polish, that being associated with mathematics and mathematicians begets. In the
modern day, probability theory has been used in several important ²elds and has led to numerous
advancements in science and technology. This list makes for a very impressive reading – with
topics ranging from the foundations of modern physics as we know it, to cryptography, weather
predictions, stock markets, going all the way to fantasy football player–prices!
The key idea here, is to take into account the information available about a certain system, and
make a prediction concerning its behavior under some operating conditions, based on historical
con²dence or logical arguments. Indeed, having been brought up with a deterministic view of the
laws of physics, one may tend to think that such a theory based on inadequate ²rst principles
is
not correct
. However, it is pertinent to note here that the laws of physics themselves are, but
a mathematical description of reality. They merely approximate the system very reliably, under
certain operating conditions, to yield results that are within an acceptable error limit. As an
*
santosha@purdue.edu
. Some rights reserved
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