Refer to Exercise 23. Assume that if m = 0, the value s = 1.5 is sent, and if m = 1, the

Chapter 4, Problem 24

(choose chapter or problem)

Refer to Exercise 23. 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 , where \(X=s+E, \text { and } E \sim N(0,0.64)\). If \(X \leq 0.5\), 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 \(601 s \text { and } 400 \mathrm{~s}\) 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

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Text Transcription:

m=0

s=-1.5

m=1

s=1.5

X=s+E, and  E \sim N(0,0.64)

X \leq 0.5

m=0

X>0.5

m=1

m=0

m=1

m=1

m=0

601 s and  400 s