Lecture11_ChebyMarkovTransform

Lecture11_ChebyMarkovTransform - ECE 340 Probabilistic...

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1 ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Prof. Vince Calhoun Prof. Vince Calhoun Lecture 11: Lecture 11: Chebychev Chebychev , Markov, , Markov, Transform Transform
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2 Quiz • Write the pdf of a Gaussian random variable • What’s the difference between a normal random variable and a standard normal random variable
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3 Reading • This class: Section 4.6-4.7 • Next class: Section 5.1-5.2
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4 Functions of RVs
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17 Markov inequality • Markov's inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant. • Markov's inequality (and other similar inequalities) relate probabilities to expectations, and provide (frequently) loose but still useful bounds for the cumulative distribution function of a random variable.
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18 Markov inequality • if X is any random variable and a > 0, then
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19 Proof: For a>0. let Taking expectation of the above = otherwise , 0 if , 1 a X I Since 0, X XI a ≥≤ [] a
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This note was uploaded on 02/10/2010 for the course TBE 2300 taught by Professor Cudeback during the Spring '10 term at Webber.

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Lecture11_ChebyMarkovTransform - ECE 340 Probabilistic...

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