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Problem 8.45 A telegraph system (an early version of digital communications) transmits either a dot or dash signal. Assume the transmission properties are such that 2/5 of the dots and 1/3 of the dashes are received incorrectly. Suppose the ratio of transmitted dots to transmitted dashes is 5 to 3. What is the probability that a received signal as the transmitted if: a) The received signal is a dot? b) The received signal is a dash? Solution (a) Let X represent the transmitted signal and Y represent the received signal. Then by application of Bayes\u2019 rule ( ) ( ) ( ) ( )( ) ( )( ) 2 1 8 1 8 3 3 1 8 3 5 3 8 5 errordasherror|dash)errordotNo(errorNo|dotdot =+= += =+=== PPPPP XXY (b) Similarly, [ ] [ ] ( ) ( ) [ ][ ] 2 1 8 2 8 2 5 2 8 5 3 2 8 3 errordotdoterrordashnoerror no|dashdash =+= +\u22c5= =+=== PPPPP XXY Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. page\u20268-55