Consider a transmission method for which the probability of a transmission error in any digit is p.
(a) Compute the probability of no errors when an uncoded 4-digit message word is sent.
(b) Compute the probability that a word is correctly decoded by the (4, 7)-Hamming code.
(c) Show that the answer to (a) does not exceed the answer to (b) if p satisfies 0 ≤ p < .5.
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