131B_1_midterm

131B_1_midterm - EE 131B Spring 09 Midterm, April 28th Open...

This preview shows pages 1–6. Sign up to view the full content.

EE 131B Spring 09 Midterm, April 28th Open book Your Name: Your ID Number: 1

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

View Full Document
1. X ( ω ) is a random variable with exponential distribution, i.e. p ( x ) = λe - λx ,λ > 0 ,x 0 . Find the characteristic function C ( t ), and its 1st, 2nd and 3rd moments (derive them from characteristic function). 2
2. X ( t,ω ) is random process with zero mean and covariance function R ( t 1 ,t 2 ). Express E [ | X ( t 2 ) - X ( t 1 ) | 2 ] in terms of R ( t 1 ,t 2 ). 3

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

View Full Document
3. z ( t,ω ) is random process and z ( t,ω ) = x ( ω ) sin ζt + y ( ω ) cos ζt. ζ is given. x ( ω ) and y ( ω ) are i.i.d. Gaussian random variable with zero mean and variance σ 2 . Find the mean and covariance of this process. 4
4. Given the process: x ( t,ω

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

131B_1_midterm - EE 131B Spring 09 Midterm, April 28th Open...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online