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Chapter3_2 - Continuous Random Variables Reading Chapter...

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1 Continuous Random Variables Reading: Chapter 3.1 – 3.8 Homework: 3.1.2, 3.2.1, 3.2.4, 3.3.2, 3.3.7, 3.4.4, 3.4.5, 3.4.9, 3.5.3., 3.5.6 G. Qu ENEE 324 Engineering Probability 2 Continuous E[X] = (a+b)/2 Var[X] = (b-a) 2 /12 Uniform Random Variable Discrete E[X] = (a+b)/2 Var[X] = (b-a)(b-a+2)/12 + = + - = otherwise b a a x a b x P X 0 ,..., 1 , 1 1 ) (   > + - + - < = b x b x a a b a x a x x F X 1 1 1 0 ) ( - = otherwise b x a a b x f X 0 1 ) ( > - - < = b x b x a a b a x a x x F X 1 0 ) (
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2 G. Qu ENEE 324 Engineering Probability 3 Example: Quiz 3.4* X: uniform continuous r.v. E[X] = 3 Var[X] = 3 Find PDF. Solve for a and b with a<b E[X]=(a+b)/2 = 3 Var[X] = (a-b) 2 /12 = 3 a=0, b=6 = otherwise x x f X 0 6 0 6 1 ) ( G. Qu ENEE 324 Engineering Probability 4 Continuous ( λ >0) E[X] = 1/ λ Var[X] = 1/ λ 2 Exponential Random Variable < = - 0 0 0 ) ( x x e x f x X λ λ - = - otherwise x e x F x X 0 0 1 ) ( λ discretization ( λ >0) K = X : discrete r.v.
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