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Solutions Manual

to accompany

Probability,Random Variables

andStochastic Processes

Fourth Edition

Athanasios PapoulisPolytechnic University

S. Unnikrishna PillaiPolytechnic University

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Solutions Manual to accompany

PROBABILITY, RANDOM VARIABLES AND STOCHASTIC PROCESSES, FOURTH EDITION

ATHANASIOS PAPOULIS

Published by McGraw-Hill Higher Education, an imprint of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas,

New York, NY 10020. Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

The contents, or parts thereof, may be reproduced in print form solely for classroom use with PROBABILITY, RANDOM

VARIABLES AND STOCHASTIC PROCESSES, FOURTH EDITION, provided such reproductions bear copyright notice, but may

not be reproduced in any other form or for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc.,

including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

www.mhhe.com

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Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

102/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

103/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

104/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

105/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

106/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

107/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

108/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

109/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

110/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

111/186

8/4/2019 Probability Random 4 e Papoulis Solution

112/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

113/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

114/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

115/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

116/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

117/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

118/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

119/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

120/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

121/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

122/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

123/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

124/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

125/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

126/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

127/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

128/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

129/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

130/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

131/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

132/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

133/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

134/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

135/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

136/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

137/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

138/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

139/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

140/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

141/186

8/4/2019 Probability Random 4 e Papoulis Solution

142/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

143/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

144/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

145/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

146/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

147/186

8/4/2019 Probability Random 4 e Papoulis Solution

148/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

149/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

150/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

151/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

152/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

153/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

154/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

155/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

156/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

157/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

158/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

159/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

160/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

161/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

162/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

163/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

164/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

165/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

166/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

167/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

168/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

169/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

170/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

171/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

172/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

173/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

174/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

175/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

176/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

177/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

178/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

179/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

180/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

181/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

182/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

183/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

184/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

185/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html

Trial version of ABC Amber PDF Merger, http://www.processtext.com/abcpdfmg.html

8/4/2019 Probability Random 4 e Papoulis Solution

186/186

Trial version of ABC Amber PDF Merger v3.03, http://www.processtext.com/abcpdfmg.html