An info source produces 0 and 1 with probabilities 0.3 and 0.7, respectively. the output of...
An info source produces 0 and 1 with probabilities 0.3 and 0.7, respectively. the output of the source is transmitted via a channel that has probabilities of error (turning a 1 into a 0 or a 0 into a 1) equal to 0.2
1) what is the probability that at the output a 1 is observed?
2) What is the probability that a 1 was output of the source if at the output of the channel a 1 is observed.
Homework Answers
Answer:
a)
Given,
To determine the probability that at the output a 1 is observed
i.e.,
= probability that 1 is produced and correctly transmitted + probability that 0 is produced and it is transmitted incorrectly
= 0.7 * (1 - 0.2) + 0.3 * 0.2
= 0.56 + 0.06
Required probability = 0.62
b)
Now to determine the probability that 1 was output of the source if
at the output of the channel a 1 is observed.
= 0.7*0.8/0.62
= 0.7 * 1.290323
= 0.903225806
= 0.9032
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