A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-1 Chapter 6: Vector Random Variables 6.1 Vector Random Variables 6.1 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-2 6.2 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-3 6.3 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-4 6.4 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-5 6.5 (b) © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-6 (c) © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-7 6.6 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-8 6.7 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-9 6.8 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-10 6.9 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-87 6.84 (a) (b) The following Octave code generates a sequence of 1000 samples: X = normal_rnd(0, 1, 1, 1000); Y = (X + [0 X(1:length(X)-1)])./2; cov(Y); © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-88 6.85 6.86 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-89 6.87 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-90 6.88 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-91 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-92 Problems Requiring Cumulative Knowledge 6.89 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-93 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-94 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-95 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-96 6.90 b) © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-97 6.91 6.92 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-98 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-99 6.93 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-100 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-101 © 2008 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458 ... INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6.2 6-22 Functions of Several Random Variables 6.18 6.19 © 2008 Pearson Education, Inc., Upper... Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-3 6.3 © 2008 Pearson Education, Inc., Upper Saddle... Saddle River, NJ 07458 A Leon-Garcia INSTRUCTOR’S SOLUTIONS MANUAL Probability, Statistics, and Random Processes for Electrical Engineering 6-4 6.4 © 2008 Pearson Education, Inc., Upper Saddle