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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online