mtsample

mtsample - Z = | X-Y | 3(20 points Multiplicative noise...

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

View Full Document Right Arrow Icon
EE 278 Saturday, July 18, 2009 Statistical Signal Processing Handout #8 Sample Midterm This is a sample midterm. 1. (20 points) Inequalities. Label each of the following statements with =, , , or None . Label a statement with = if equality always holds. Label a statement with or if the corresponding inequality holds in general and strict inequality holds sometimes. If no such equality or inequality holds in general, label the statement as None . You have to justify your answers. a. (2 points) P( A | B ) vs. P( B | A ) b. (2 points) p X ( x ) vs. p X,Y ( x,y ) for X and Y discrete random variables. c. (2 points) f X ( x ) vs. f X,Y ( x,y ) for X and Y continuous random variables. d. (3 points) E p X 1 X 1 + X 2 P + E p X 2 X 1 + X 2 P vs. 1. e. (3 points) E( X log 2 X ) vs. 2 if X > 0 and E ( X ) = 2. f. (4 points) P { ( XY ) 2 > 16 } vs. 1 / 8 if E( X 4 ) = E( Y 4 ) = 2. g. (4 points) E(Var( X | Y 2 )) vs. E(Var( X | Y )). 2. (15 points) Function of exponential random variables. Let X and Y be independent exponen- tially distributed random variables with parameter λ . Find the pdf of the random variable
Background image of page 1

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

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

Unformatted text preview: Z = | X-Y | . 3. (20 points) Multiplicative noise channel. The signal X and the noise Z are independent random variables and each is uniform in the interval (0 , 1). We observe the output Y = XZ . a. (10 points) Find the joint pdf of the random variables X and Y . b. (10 points) Find the MMSE estimate of X given Y . 4. (20 points) Fading channel. Let the signal X = b 1 with probability 1 / 2 2 with probability 1 / 2 and the channel gain A with pdf f A ( a ) = b λe-λa a ≥ otherwise be independent random variables. The channel output Y = AX is observed. a. (10 points) Find the optimal decoding rule D ( y ) for deciding whether X = 1 or 2, i.e., the rule that minimizes the probability of decoding error. b. (10 points) Find the probability of error for the decoding rule in part (a). Page 2 of 2 EE 278, Spring 2009...
View Full Document

This note was uploaded on 05/20/2011 for the course EE 278 taught by Professor Balajiprabhakar during the Winter '09 term at Stanford.

Page1 / 2

mtsample - Z = | X-Y | 3(20 points Multiplicative noise...

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