This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Communication Systems EE 132A UCLA Winter quarter 2011/2012 Prof. Suhas Diggavi Handout # 4, Due: Thursday, January 19, 2012 Homework Set # 1 Problem 1 (Basic Probabilities) Find the following probabilities. (a) A box contains m white and n black balls. Suppose k balls are drawn. Find the probability of drawing at least one white ball. (b) We have two coins; the first is fair and the second is twoheaded. We pick one of the coins at random, we toss it twice and heads shows both times. Find the probability that the coin is fair. Hint: Define X as the random variable that takes value 0 when the coin is fair and 1 otherwise. Problem 2 (Correlation versus Independence) Let Z be a random variable with p.d.f.: f Z ( z ) = 1 / 2 , 1 z 1 , otherwise . Also, let X = Z and Y = Z 2 . (a) Show that X and Y are uncorrelated. (b) Are X and Y independent? (c) Now let X and Y be jointly Gaussian, zero mean, uncorrelated with variances 2 X and 2 Y respectively. Are X and Y independent? Justify your answer.independent?...
View
Full
Document
This note was uploaded on 04/03/2012 for the course EE 199 taught by Professor Liu during the Spring '10 term at UCLA.
 Spring '10
 Liu

Click to edit the document details