Detection in a binary symmetric channel (28 points) a signal x ∈ {0, 1} is transmitted through a binary symmetric channel with crossover probability p. assume x = 0 or 1 with equal probability. suppose x is sent n times, each time the channel output yi follows yi = x ⊕ zi , where "⊕" is the modulo 2 addition, and zi ’s are independent bern(p) random variables. further assume x and all zi ’s are independent.