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# sm8_45

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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

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page\u20268-55```