L8 - RANDOM VARIABLES Measurements and observations are called random variables Each results from an outcome of an experiment so Definition Random

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Unformatted text preview: RANDOM VARIABLES Measurements and observations are called random variables. Each results from an outcome of an experiment, so: Definition: Random variable X is real function on sample space S. Start with discrete r.v. R X is finite or countable. 1 For any real x ∈ R X , the set { X = x } is an event and so has a probability. Definition: The probability mass func- tion of X is the function f ( x ) = P ( X = x ) Properties. • f ( x ) ≥ • ∑ x ∈R X f ( x ) = 1 • P ( X ∈ A ) = ∑ x ∈ A f ( x ) 2 Example: Benford’s law First observed by Frank Benford working at GE Research Laboratories in 1920s. In many real-world datasets the first digit of a number follows a distribution: First Digit 1 2 3 4 5 Probability 0.301 0.176 0.125 0.097 0.079 First Digit 6 7 8 9 Probability 0.067 0.058 0.051 0.046 Consider a market capital of a randomly picked publicly traded company. Let X = first digit of market capital amount....
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This note was uploaded on 01/03/2012 for the course EE 1244 taught by Professor Drera during the Fall '10 term at Conestoga.

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L8 - RANDOM VARIABLES Measurements and observations are called random variables Each results from an outcome of an experiment so Definition Random

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