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A binary message m, where m is equal either to 0 or to 1, is sent...

A binary message m, where m is equal either to 0 or to 1, is sent over an information channel. Because of noise in the channel, the message received is X, where X = m + E, and E is a random variable representing the channel noise. Assume that if X ≤ 0.5 then the receiver concludes that m = 0 and that if X > 0.5 then the receiver concludes that m = 1. Assume that E ∼ N(0, 0.24).

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?

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