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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’ 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

=+=
+⋅=

=+=== PPPPP XXY

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page…8-55```