Lecture13_Spring11

Lecture13_Spring11 - Elec210: Lecture 13 Multiple random...

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Elec210 Lecture 13 1 Elec210: Lecture 13 Multiple random variables (RVs) Joint probability mass function of two discrete RVs Marginal probability mass function
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Elec210 Lecture 13 2 Vector Random Variables A vector random variable is a function that assigns a vector of real numbers to every outcome of an experiment. X 1 X 2 X 3 S X 1 X 2 X 3 X X
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Elec210 Lecture 13 3 Example: Height, Weight, Age Example 5.1 – A student’s name is selected randomly from an urn. Let denote the outcome of this experiment, and define: H ( ) = height of student in inches W ( ) = weight of student in pounds A ( ) = age of student in years The vector ( H ( ) , W ( ) , A ( ) ) is a vector random variable
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Elec210 Lecture 13 4 Example: Sampled Voltage (ADC) Example – Let the outcome of an experiment be a voltage waveform X ( t ). Let the random variable X k = X ( kT ) be the sampled voltage taken at time t = kT . The vector consisting of the first n samples is a vector random variable. ) , X , , X , X (X X n 3 2 1
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Elec210 Lecture 13 5 Example: Skin Detection in Digital Images Refer to Poster Question: What about detecting: Eyes? Face? Multiple Faces?
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Elec210 Lecture 13 6 Two Random Variables One random variable can be considered as a mapping from the sample space to the real line . Two random variables can be considered as a mapping from the sample space to the plane . Note that given the outcome of the experiment, both X and Y are determined simultaneously .
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Scattergrams Scattergrams are used to visualize the joint behavior of two random variables. A set of experiments is performed. For each experiment, we place a dot at every observation pair ( x , y ). Elec210 Lecture 13 7
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Scattergrams: Example Elec210 Lecture 13 8
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Scattergrams: Mobile Communications! Elec210 Lecture 13 9 Q: What is the distribution of the noise?
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Events involving two RVs Events involving two random variables are regions in the X-Y plane. You can find the region using the following procedure Find the boundaries of the event. The boundary splits the plane into one or more regions.
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This note was uploaded on 03/27/2011 for the course ELEC 202 taught by Professor ? during the Spring '11 term at HKUST.

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Lecture13_Spring11 - Elec210: Lecture 13 Multiple random...

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