4.Consider the BPSK system whose transmitted signal is given by \[ x(t) = \begin{cases} A \cos(2\pi f_c t), & m = 0, \\ -A \cos(2\pi f_c t), & m = 1, \end{cases} \quad 0 \le t \le T, \quad f_c \gg \frac{1}{T}, \] The message \( m \) has the distribution of \( \mathbb{P}(m = 0) = 4/9 \) and \( \mathbb{P}(m = 1) = 5/9 \). The received signal is given by \( y(t) = x(t) + n(t) \) where \( n(t) \) is a zero mean white Gaussian noise with power spectral density \( N_0/2 \) for all \( f \).