1. In the communication system below the probability of transmitting ("B" before) symbols 1 and are: P(B1) = 0.7 and P(B0) =0.3. At the receiver (“A", after), when symbol 1 is sent, the conditional probabilities of reception of 1

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1. In the communication system below the probability of transmitting ("B" before) symbols 1 and 0
are:
P(B1) = 0.7 and P(B0)= 0.3.
At the receiver ("“A", after), when symbol 1 is sent, the conditional probabilities of reception of 1 or 0
are: P(A1/ B1) = 0.8 and P(A0/ B1) =0.2
When symbol 0 is sent the conditional probabilities of reception of 0 or 1 are:
P(40/ BO) = 0.9 and P(Al/ BO) = 0.1
a) Find the total probability of reception of symbol 1 P(Al) and the total probability of reception of
symbol 0 P(A0)
b) Find the probability of transmission of symbol 1 when symbol 0 is received, P(B1/ A0) and the
probability of transmission of symbol 0 when symbol 1 is received, P(B0/ Al)
c) Find the total probability of error in reception
B1
A1
P(B1)=0.7
P(A1/B1)=0.8
P(AO/B1)=0.2
P(A1/BO)=0.1
P(AO/BO)=0.9
B0
농 AO
P(BO)=0.3
Transcribed Image Text:1. In the communication system below the probability of transmitting ("B" before) symbols 1 and 0 are: P(B1) = 0.7 and P(B0)= 0.3. At the receiver ("“A", after), when symbol 1 is sent, the conditional probabilities of reception of 1 or 0 are: P(A1/ B1) = 0.8 and P(A0/ B1) =0.2 When symbol 0 is sent the conditional probabilities of reception of 0 or 1 are: P(40/ BO) = 0.9 and P(Al/ BO) = 0.1 a) Find the total probability of reception of symbol 1 P(Al) and the total probability of reception of symbol 0 P(A0) b) Find the probability of transmission of symbol 1 when symbol 0 is received, P(B1/ A0) and the probability of transmission of symbol 0 when symbol 1 is received, P(B0/ Al) c) Find the total probability of error in reception B1 A1 P(B1)=0.7 P(A1/B1)=0.8 P(AO/B1)=0.2 P(A1/BO)=0.1 P(AO/BO)=0.9 B0 농 AO P(BO)=0.3
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