Elec2600: Lecture 21
Central Limit Theorem
The PDF of sums of Random Variables
The characteristic function
Proof of the Central Limit Theorem
Elec2600 Lecture 21
http:/www.mathsisfun.com/data/quincunx.html
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Central Limit Theorem
Any distribution
Supp
Elec2600: Lecture 17
One function of two random variables
Discrete random variables
Continuous random variables
Using conditioning
Thus far, for Z = g(X,Y), with X and Y
random variables, we know how to
compute the moments of Z.
But how do we compute the
Elec2600: Lecture 16
Conditional Probability
Conditional Expectation
Elec2600 Lecture 16
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Conditional Probability Mass Functions
Suppose that X and Y are discrete RVs assuming integer values.
The conditional pmf of Y given X is
pY | X (k | j )
P Y k
Elec2600: Lecture 13
Multiple random variables (RVs)
Joint probability mass function of two discrete RVs
Marginal probability mass function
Elec2600 Lecture 13
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Vector Random Variables
A vector random variable X is a function that assigns a vector
of
Elec2600 Lecture 12
MATLAB functions for continuous random variables
Functions (Transformations) of a Random Variable
Elec2600 Lecture 12
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MATLAB Functions for Continuous RVs
Generating m by n arrays of random samples
unifrnd(a,b,m,n)
exprnd(1/lambda,
Elec2600 Lecture 11
Expectation of Continuous Random Variables
Variance of Continuous Random Variables
Important Continuous Random Variables
Elec2600 Lecture 11
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Review: Expectation
Interpretation
The average value of a random variable if we repeat
Elec 2600: Lecture 10
Single random variables: discrete, continuous and mixed
Continuous R.V. and Cumulative Distribution Function (CDF)
Probability Density Function (PDF)
Conditional CDFs and PDFs
Elec2600 Lecture 10
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Random Variables: Review
A random
Elec 2600: Lecture 9
Important discrete random variables
Summary of variables you know:
Bernoulli
Binomial
Geometric
Discrete Uniform
New random variable: Poisson
MATLAB commands for plotting probability mass functions
and generating discrete random v
Elec 2600: Lecture 8
Conditional Probability Mass Function
Conditional Expected Value
Conditional Poker Hand
Elec2600 Lecture 8
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Conditional Probability Mass Function
The effect of partial information about the outcome of a random
experiment on the p
Elec 2600: Lecture 7
Expectation of a random variable
Expected value of a function of a random
variable
Variance of a random variable
Moments of a random variable
The human brain weighs
1500 grams, on average.
Elec2600 Lecture 7
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Interesting Fact Ein
Elec 2600: Lecture 6
Random Variables
Equivalent events
Discrete Random Variables
Probability mass function
Elec2600 Lecture 6
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Random Variables
A random variable
X is a function that assigns a number to every
outcome of an experiment.
The function
ELEC 2600:
Probability and Random Processes in
Engineering
Spring 2013
Instructor: Prof. Jun ZHANG
Office: Rm 2448 (Lift 25-26)
Tel: 2358 7050
Email: [email protected]
Webpage: http:/www.ece.ust.hk/~eejzhang/
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Elec 2600: Lecture 1
Course Details
Models i