Elec210: Lecture 26
Stationary Random Processes
Wide Sense Stationary (WSS) Random Processes
Elec210 Lecture 26
1
Stationary Random Processes
Definition: A process is stationary if the joint distribut
Elec210: Lecture 25
Continuous Time I.S.I. Random Processes
Poisson Random Process
Additional Random Processes (FYI)
Random Telegraph Process
Shot Noise Process
Weiner Process
Elec210 Lecture 25
1
Elec210: Lecture 24
Discrete Time Random Processes
Sum Processes
ISI Processes
Elec210 Lecture 24
1
Sum Random Processes
Definition: A sum process Sn is obtained by taking the sum of
all past valu
Elec210: Lecture 23
Mean and Variance
Correlation and Covariance Functions
Multiple Random Processes
Elec210 Lecture 23
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Mean and Variance Functions
Mean
mX (t ) E[ X (t )] xf X ( t ) ( x) dx
Var
Elec210: Lecture 22
Definition of a Random Process
Specification of a Random Process
Elec210 Lecture 22
1
Definition of a Random Process
Definition: A random process or
stochastic process maps a
pro
Elec210: Lecture 21
Central Limit Theorem
The PDF of sums of Random Variables
The characteristic function
Proof of the Central Limit Theorem
Elec210 Lecture 21
http:/www.mathsisfun.com/data/quincu
Elec210: Lecture 20
Sums of Random Variables
Mean and Variance of Sample Means
Useful Inequalities
Laws of Large Numbers
Elec210 Lecture 20
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Sums of Random Variables
For any set of random variab
Elec210: Lecture 19
Single Gaussian Random Variable
Gaussian Random Vectors
Elec210 Lecture 19
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Gaussian Random Variable
The Gaussian random variable is
used to model variables that tend
to occur
Elec210: 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 t
Elec210: Lecture 16
Conditional Probability
Conditional Expectation
Elec210 Lecture 16
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Conditional Probability Mass Functions
Suppose that X and Y are discrete RVs assuming integer values.
The c
Elec210: Lecture 15
Independence
Expectation of Function of 2 Variables
Joint Moments
Elec210 Lecture 15
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Independence
Definition: Two random variables X and Y are said to be
independent or stati
Elec210: Lecture 14
Pairs of continuous random variables
Review of 2D functions, differentiation and integration
Joint cumulative distribution function
Joint probability density function
Elec210 L