# soln7 - Probability and Stochastic Processes: A Friendly...

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Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers Roy D. Yates and David J. Goodman Problem Solutions : Yates and Goodman,4.4.2 4.5.1 4.6.2 4.7.3 and 4.4.10 I’m including 4.4.10 because the solution to 4.7.3 references the solution to this problem. 4.4.10 was NOT assigned. Problem 4.4.2 Erlang random variable X with parameters λ > 0 and n has PDF f X ( x ) = ½ λ n x n - 1 e - λ x / ( n - 1 ) ! x 0 0 otherwise In addition, the mean and variance of X are E [ X ] = n λ Var [ X ] = n λ 2 (a) Since λ = 1 / 3 and E [ X ] = n / λ = 15, we must have n = 5. (b) Substituting the parameters n = 5 and λ = 1 / 3 into the given PDF, we obtain f X ( x ) = ½ ( 1 / 3 ) 5 x 4 e - x / 3 / 24 x 0 0 otherwise (c) From above, we know that Var [ X ] = n / λ 2 = 45. Problem 4.5.1 Given that the peak temperature, T , is a Gaussian random variable with mean 85 and standard devi- ation 10 we can use the fact that F T ( t ) = Φ (( t - μ T ) / σ T ) and Table 4.1 on page 142 to evaluate the

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## This note was uploaded on 03/05/2009 for the course CMPE 107 taught by Professor Marshallsylvan during the Spring '09 term at New Hampshire.

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soln7 - Probability and Stochastic Processes: A Friendly...

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