homework09

# homework09 - in the set 1 Â Â Â 9 at a 1 signiFcance level...

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Probability for Engineering Applications Assignment #9, due at the beginning of class on Thursday, March 30 th , 2006 1. (3 pts) (Textbook exercise 3.81) Compare the Chebyshev bound and the exact probability for the event {| X - m | ≥ c } as a function of c when (note that E [ X ] = m ) a. X is a uniform random variable in the interval [ - b, b ]. b. X is a Laplacian random variable with parameter a . c. X is a Gaussian random variable with zero mean and variance σ 2 . 2. (2 pts) (Textbook exercise 3.84) The following histogram was obtained by counting the occurance of the Frst digit of telephone numbers in one column of a telephone directory: digit 0 1 2 3 4 5 6 7 8 9 observed 0 0 24 2 25 3 32 15 2 2 Table 1: Number of occurances a. Test the goodness of Ft of this data to a random variable that is uniformly distributed
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Unformatted text preview: in the set { , 1 , Â· Â· Â· , 9 } at a 1% signiFcance level. b. Repeat for the set { 2 , 3 , Â· Â· Â· , 9 } . 3. (3 pts) (Textbook exercise 3.101) The lifetime T of a device has the pdf f T ( t ) = ( Î»e-Î» ( t-T ) t â‰¥ T t < T a. Â±ind the reliability and MTTÂ± of the device. b. Â±ind the failure rate function. c. How many hours of operation can be considered to achieve 99% reliability? 4. (2 pts) (Textbook exercise 3.104) The lifetime T of a device is a Rayleigh random variable. a. Â±ind the reliability of the device. b. Â±ind the failure rate function. 1...
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