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), 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 \(q\left( t \right) = \sqrt E\) φ₂ (t) for what value of E would we obtain the same bit-error probability P_b?