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.