131A_1_Lecture_6-3_Winter_2012

# 131A_1_Lecture_6-3_Winter_2012 - EE 131A Probability...

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UCLA EE131A (KY) 1 EE 131A Probability Professor Kung Yao Electrical Engineering Department University of California, Los Angeles Lecture 6-3

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UCLA EE131A (KY) 2 Continuous random variable (1) A continuous random variable X is defined as a rv whose cdf F(x) is continuous everywhere and can be expressed as an integral of a non-negative valued function f(x) such that Then the derivative of the cdf F(x) with respect to x defines the probability density function (pdf) x - F(x)= f(t)dt . dF(x) f(x) = . dx
UCLA EE131A (KY) 3 Continuous random variable (2) The pdf f(x) represents the “density” of the probability at the point x in the sense that the probability over the interval of {x < X x + h} is given by P(x<X x + h)= F(x + h) - F(x) = [(F(x + h) - F(x) )/ h] h f(x) h, when h is very small. The pdf function f(x) has various properties: 1. 0 f(x), since it is the derivative of the non-decreasing cdf F(x).

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131A_1_Lecture_6-3_Winter_2012 - EE 131A Probability...

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