HW5_Spring11

HW5_Spring11 - ELEC210 Spring 2011 Homework 5 1. Let X = U...

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

View Full Document Right Arrow Icon
1 ELEC210 Spring 2011 Homework 5 1. Let n X U = where n is a positive integer and U is a uniform random variable in the interval [-1,1]. Find the cdf and pdf of X . 2. The amplitude of a radio signal X is a Rayleigh random variable with pdf: () 22 /2 2 , 0, 0 x X x fx e x α => > Find the pdf of 3 ZX + =− ( ( ) () m a x0 , XX + = ). 3. The input X to a communication channel is “-1” or “1”, with respective probabilities 1/3 and 2/3. The output of the channel Y is equal to: the corresponding input X with probability 1 e pp −− ; - X with probability p ; 0 with probability e p . (a) Describe the underlying space S of this random experiment and show the mapping from S to XY S , the range of the pair ( X , Y ). (b) Find the probabilities for all values of ( X , Y ). (c) Find [] P XY , [ ] 0 PY = . 4. A modem transmits a two-dimensional signal ( X , Y ) given by: ( ) cos 2 / 8 Xr π and ( ) sin 2 / 8 Yr where Θ is a discrete uniform random variable in the set {0,1,2,…,7}. (a) Show the mapping from S to XY S , the range of the pair ( X , Y ).
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 10/16/2011 for the course ELEC 308,315,10 taught by Professor Prof.shenghuisong during the Spring '11 term at CUHK.

Page1 / 3

HW5_Spring11 - ELEC210 Spring 2011 Homework 5 1. Let X = U...

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