The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Summer 2013
Conditional probabilities
Interested in calculating probabilities when some partial information
about the outcome of the random experiment is available.
Example Tossing 2 dice
Suppose the first die is 3; given this information, what is the
probability tha
The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
Worked examples Basic Concepts of Probability Theory
Example 1 A regular tetrahedron is a body that has four faces and, if is tossed, the
probability that it lands on any face is 1/4. Suppose that one face of a regular tetrahedron
has three colors: red, g
The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
Worked examples Multiple Random Variables
Example 1
Let X and Y be random variables that take on values from the set cfw_1, 0, 1.
(a) Find a joint probability mass assignment for which X and Y are independent, and
conrm that X 2 and Y 2 are then also inde
The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2015
ISOM 1500 Term Project Guidelines
As you know, a total of 15 points (out of 100) are reserved for your term project for
the ISOM 1500 group project. So here are some additional guidelines, in case they
help you as you complete your group project.
The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
Markov Processes
In general, the probability structure of a random sequence (discrete parameter
random process) is determined by the joint probabilities
P [X0 = j0, X1 = j1, , Xn = jn].
If it happens that
P [Xn = jnXn1 = jn1, , X0 = j0] = P [Xn = jnXn1
The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Summer 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
Random experiments
A random experiment is a process characterized by the following
properties:
(i) It is performed according to some set of rules,
(ii) It can be repeated arbitrarily often,
(iii) The result of each performance depends on chance and cannot
The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
Random variables
Some random experiments may yield a sample space whose elements
(events) are numbers, but some do not. For mathematical purposes, it is
desirable to have numbers associated with the outcomes.
A random variable X is a function that assigns
The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2013
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The Hong Kong University of Science and Technology
Probability and Random Processes
MATH 246

Fall 2015
We will use the following rubric to guide us in evaluating your project video. Note
that this is just a framework that will guide the evaluation, and your actual score
could be slightly different from the rubric below.
CATEGORY
Content (10 points)