Mathematics, 02.11.2019 06:31, badaxz

Alice is trying to transmit to bob the answer to a yes-no question, using a noisy channel. she encodes "yes" as 1 and "no" as 0, and sends the appropriate value. however, the channel adds noise; speciﬁcally, bob receives what alice sends plus a n(0,σ2) noise term (the noise is independent of what alice sends). if bob receives a value greater than 1/2 he interprets it as "yes"; otherwise, he interprets it as "no". (a) find the probability that bob understands alice correctly. (b) what happens to the result from (a) if σ is very small? what about if σ is very large? explain intuitively why the results in these extreme cases make sense.

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Alice is trying to transmit to bob the answer to a yes-no question, using a noisy channel. she encod...