Lecture10_ContinuousRVFamilies

Lecture10_ContinuousRVFamilies - 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 10: Continuous RV Families Lecture 10: Continuous RV Families
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2 Reading • This class: Section 4.4-4.5 • Next class: Section 4.6-4.7
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3 Homework • 3.9, 3.49, 4.5, 4.12, 4.14 • Plus problems on handout…
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4 Outline Section 4.4-4.5 Important continuous RV’s •U n i f o r m Exponential •G a u s s i a n a m m a Rayleigh •C a u c h y laplacian Functions of RV’s
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5 Common families of Continuous Distribution As mentioned previously, the development of the probability distribution of a continuous random variable is not as intuitive as in the discrete case. Thus, we will concentrate on exploring several common families of distributions, which fit a wide range of experiments
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6 The Uniform Distribution o The simplest distribution is the one in which a continuous r.v. can assume any value within a interval [a, b] ± Def: A continuous r.v. X is said to have a uniform distribution on the interval [a,b] if the probability distribution (pdf) of X is: = otherwise b x a a b x f 0 1 ) (
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7 The Uniform Distribution The cumulative distribution is 12 ) ( ) ( 2 ) 1 ( ) ( ] [ ) ( ) ( ) ( ) ( 2 a b X V a b dx a b x dx x xf X E a b a x a b a a b x a x a b x dx x f dx x f x X P X F x x x x = + = = = = = = = = =
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8 The Uniform Distribution Note: An important uniform distribution is that for when a = 0 and b = 1, namely U(0, 1) A U(0,1) r.v. can be used to simulate observation of other random variables of the discrete and continuous type.
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9 Exponential Distribution
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Lecture10_ContinuousRVFamilies - ECE 340 Probabilistic...

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