Question

Question 2:

For a certain binary channel, the probability that the transmitted ‘0’ was correctively received as ‘0’ is 0.94 and the probability that the transmitted ‘1’ was received as ‘1’ is 0.91. Further, the probability of transmitting ‘0’ is 0.45. If a signal is sent, determine

(i) the probability that a ‘0’ was received ;

(ii) the probability that a ‘0’ was transmitted given that a ‘0’ was received, and

(iii) the probability of an error.

Answer 1

from the question we have the following values
P(0 recieved | 0 transmitted) = 0.94 = 1 - P(1 recieved | 0 transmitted)
P(1 recieved | 1 transmitted) = 0.91 = 1 - P(0 recieved | 1 transmitted)
P(0 transmitted) = 0.45 = 1 - P(1 transmitted)

i) P(0 is recieved) = P(0 recieved | 0 transmitted)*P(0 transmitted) + P(0 recieved | 1 transmitted)*P(1 transmitted)
= 0.94*0.45 + 0.09*0.55
= 0.4725

ii) P(0 transmitted | 0 recieved) = P(0 recieved | 0 transmitted)*P(0 transmitted) / P(0 is recieved)
= (0.94*0.45) / 0.4725
= 0.8952

iii) P(error) = P(1 recieved | 0 transmitted) + P(0 recieved | 1 transmitted)
= 0.06 + 0.09
= 0.15

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