Download Week 1: Descriptive Statistics

Preliminaries and
Introduction to
Probability
CEE 11 Spring 2002
Dr. Amelia Regan
TA Riju Lavanya
Preliminaries
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The syllabus and other important information
for this class is posted on the eee server at
eee.uci.edu.
Several unannounced quizzes will be held on
Tuesdays
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This course package contains a summary of
the notes for each topic covered.
Preliminaries
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Calculators with statistical functions are fine
for getting the job done -- not for learning
probability
No calculators are allowed in the midterm
Probability
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An informal definition of probability is a
numerical value or the “chance” of
occurrence of several possible outcomes of
an unpredictable event.
Engineers study probability because
uncertainties are unavoidable in the design
and planning of engineering systems
Probability

Understanding probability and statistics is
also important for getting along in the world
 for
understanding business reports, claims
found in newspaper articles etc.
 for being able to distinguish between
“coincidences that are likely and those that
are not.
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Studying probability helps to gain intuition
into mathematical modeling -- and to
understand when intuition is likely to fail
 Several
counter intuitive examples follow
An example
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How many people would we have to gather
in a room to be sure that at least two of
them share the same birthday?
Answer: 367 (don’t forget feb 29th)
How many people would we have to gather
in a room so that the chance that two of
them have the same birthday is 50%?
Answer: 23
Solution
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The probability that two people in a room do
not have the same birthday is
 365  364 



365
365


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The probability that five people in a room do
not have the same birthday is
 365  364  363  362  361 






365
365
365
365
365






Solution
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We simply subtract these probabilities from
1.0 to get the complementary probability
that if 2,3,…n people are in a room that at
least two have the same birthday
For n = 23 the probability is ~ 0.507
For n = 50, the approximate size of this
class, the probability is 0.97