A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density N₀/2. Binary signaling, with 0↦p(t) and 1↦q(t), is used for the transmission, along with an optimal receiver that minimizes the bit-error probability. Let φ₁(t) and φ₂(t) form an orthonormal signal set. If we choose p(t)=φ₁(t) and q(t)=-φ₁(t) we would obtain a certain bit-error probability P_b. If we keep p(t)=φ₁(t), but take q(t)=√Eφ₂(t) for what value of E would we obtain the same bit-error probability P_b?