Course Credit:
4
Course Description :
This is an introductory course on probability theory. This course attempts to provide basic
concepts of set theory, experiment and sample space, and di erent approaches of de ning
probability. It discusses useful laws of probability, conditional probability, Bayes rule, random
variables and their distributions, and functions of random valuables. It also covers discussions
on certain operators like mathematical expectation and generating function with properties
and applications, and thorough discussions on commonly used probability distributions such
as binomial, hypergeometric, and negative binomial, Poisson, normal, exponential and gamma
distributions.
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Course Objectives
To provide basic concepts of sets, counting techniques, and acquaint students with necessary
skills for solving probability related problems using appropriate laws. To introduce the notions
of random variables. To develop ability to nd probability distribution of random variables
and of their functions. To introduce operators like generating functions, expectation, etc.
for studying the characteristics of distributions. To make familiar with basic probability
distributions with possible areas of applications. To prepare the students for learning advance
courses where probability theory has a prominent role.
Course Learning Outcomes (CLOs)
Students who successfully complete this course should be able to
CLO1 understand (explain ideas and concept) Students will be able to explain basic con-
cepts of set theory, experiment and sample space, di erent approaches of de ning
probability, and useful laws of probability.
CLO2 analyze (draw connection among ideas) Students will be able to analyze and draw
connections between concepts such as conditional probability, Bayes rule, random
variables, and their distributions.
CLO3 evaluate (justify a stand or decision) Students will be able to justify their decisions
by evaluating the probability distributions of random variables and the use of
operators like mathematical expectation and generating functions.
CLO4 apply (use information in new situation) Students will be able to apply the concepts
and laws of probability to solve problems and nd probability distributions of
random variables in new situations.
CLO5 create (produce a new or original work) Students will be able to create new insights
and original work by using generating functions and studying characteristics of
various probability distributions.
Program Learning Outcomes (PLOs)
CLOs PLO1 PLO2 PLO3 PLO4 PLO5 PLO6 PLO7 PLO8
CLO1 3 2 3 2 1 2 1 1
CLO2 2 3 3 3 2 2 1 1
CLO3 2 2 3 3 2 3 1 1
CLO4 2 2 2 3 2 3 1 1
CLO5 2 2 3 3 2 2 2 1
Contents
Combinatorial analysis: basic principles of counting, permutations, combinations; axioms of
probability: sample space and events, axioms of probability, sample spaces having equally
likely outcomes, probability as a measure of belief; conditional probability and independence:
conditional probabilities, Bayes formula, independent events.
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Random variables: introduction, discrete random variables, expectation, expectation of a
function of a random variable, variance, Bernoulli and binomial random variables, Poisson
random variable, other discrete random variables (geometric, negative binomial, hypergeo-
metric); expected value of a sums of random variables; properties of cumulative distribution
function; continuous random variables: expectation and variance of continuous random vari-
able, normal random variable, normal approximation to binomial distribution, exponential
random variables.
Jointly distributed random variables: joint distribution functions, independent random vari-
ables, sums of independent random variables, conditional distributions (discrete and contin-
uous cases); properties of expectation: expectation of sums of random variables, covariance,
variance of sums, correlations, conditional expectation, moment generating functions, proba-
bility generating function.