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Suppose that a binary message M ? {1,0} is to be communicated from location A to location B via a channel, where M is a Bernoulli random variable with pM(1) = 1 ? pM(0) = q. If M = 1 we will transmit the signal X = +2, and if M = 0 we will transmit the signal X = ?2. The transmitted signal X, via channel, is corrupted by an additive normal noise W ? N(1, 2), so the received signal Y at location B is given by Y = X + W. Assume the receiver decodes the message according to the following rule: • if Y ? 1, then decode the message as M = 1; • if Y < 1, then decode the message as M = 0. Find the probability of decoding error. [You can express the answer in terms of the cumulative distribution function of a standard normal random variable ?(a) = 1/?2? ??? to a e^(?z^2/2)dz.]

          Suppose that a binary message M ? {1,0} is to be communicated from location A to location B via a channel, where M is a Bernoulli random variable with pM(1) = 1 ? pM(0) = q. If M = 1 we will transmit the signal X = +2, and if M = 0 we will transmit the signal X = ?2. The transmitted signal X, via channel, is corrupted by an additive normal noise W ? N(1, 2), so the received signal Y at location B is given by Y = X + W. Assume the receiver decodes the message according to the following rule:
• if Y ? 1, then decode the message as M = 1;
• if Y < 1, then decode the message as M = 0.
Find the probability of decoding error. [You can express the answer in terms of the cumulative distribution function of a standard normal random variable ?(a) = 1/?2? ??? to a e^(?z^2/2)dz.]

Suppose that a binary message M ? 1,0 is to be communicated from location A to location B via a channel, where M is a Bernoulli random variable with pM(1) = 1 ? pM(0) = q. If M = 1 we will transmit the signal X = +2, and if M = 0 we will transmit the signal X = ?2. The transmitted signal X, via channel, is corrupted by an additive normal noise W ? N(1, 2), so the received signal Y at location B is given by Y = X + W. Assume the receiver decodes the message according to the following rule:
• if Y ? 1, then decode the message as M = 1;
• if Y < 1, then decode the message as M = 0.
Find the probability of decoding error. [You can express the answer in terms of the cumulative distribution function of a standard normal random variable ?(a) = 1/?2? ??? to a e^(?z^2/2)dz.]

Added by Alexis C.

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