IEE380Summer09_Q4_Solutions

IEE380Summer09_Q4_Solutions - IEE 380 Summer 2009

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IEE 380 Summer 2009 Name:__________________________ Quiz #4A a. Using calculus (not your calculator) show that 2 2 3 ) ( x x f = for -1 < x < 1 is a valid probability density function. b. What is the probability that X = ½? 0, because the probability that any continuous random variable equals ANY numerical value is 0. IEE 380 Summer 2009 Name:__________________________ Quiz #4B a. Given that the probability density function of X is for -1 < x < 1, what is the probability that X < 0? Show all your work using calculus and not your calculator. . b. What is the probability that X = .33? 0, because the probability that any continuous random variable equals ANY numerical value is 0. 2 2 3 ) ( x x f = 1 6 3 dx x 2 3 ) ( 1 1 - 3 2 1 1 1 1 = = = - = - = x dx x f x x 2 1 6 3 dx x 2 3 ) ( ) 0 ( 0 1 - 3 2 0 1 0 1 = = = = < - = - = x dx x f X P x x
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IEE 380 Summer 2009 Name:__________________________ Quiz #4C The CDF of X, the length of a computer cable is given as . b. What is the probability that X > 1203?
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Unformatted text preview: IEE 380 Summer 2009 Name:__________________________ Quiz #4D The CDF of X, the length of a computer cable is given as . b. Show the probability density function for X. 1210 for x 1 1210 x 1200 for 120 10 x 1200 for x ) ( = &lt;-= = x F a. What is the probability that X = 1205? 0, because the probability that any continuous random variable equals ANY numerical value is 0. a. a. What is the probability that X = 1201? b. c. 0, because the probability that any continuous random variable equals ANY numerical value is 0. 1210 for x 1 1210 x 1200 for 120 10 x 1200 for x ) ( = &lt;-= = x F 70 . 120 10 1203 1 ) ( 1 ) 1203 ( 1 ) 1203 ( 1 = --=-= -= -= x x F X P X P 1210 x 1200 for 10 1 ) ( ) ( &lt; = = x F dx d x f...
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IEE380Summer09_Q4_Solutions - IEE 380 Summer 2009

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