Refer to Exercise 25. Assume that if m = 0, the value s = – 1.5 is sent, and if m = 1, the value s = 1.5 is sent. The value received is X, where X = s + E, and E ~ N(0, 0.64). If X ? 0.5, then the receiver concludes that m =0, and if X > 0.5, then the receiver concludes that m = 1.

a. If the true message is m = 0, what is the probability of an error, that is, what is the probability that the receiver concludes that m = 1?
b. If the true message is m = 1, what is the probability of an error, that is, what is the probability that the receiver concludes that m = 0?
c. A string consisting of 601s and 400s will be sent. A bit is chosen at random from this string. What is the probability that it will be received correctly?
d. Refer to part (c). A bit is chosen at random from the received string. Given that this bit is 1, what is the probability that the bit sent was 0?
e. Refer to part (c). A bit is chosen at random from the received string. Given that this bit is 0, what is the probability that the bit sent was 1?


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