A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_0}{2}$,

when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular time $t = t_k$, the variance of the random variable $n(t_k)$ is ________.

An amplitude modulator has output (in Volts)

$$s(t) = A \cos(400 \pi t) + B \cos(360 \pi t) + B \cos(440 \pi t)$$.

The carrier power normalized to $1\Omega$ resistance is 50 Watts. The ratio of the total sideband power to the total power is 1/9. The value of $B$ (in Volts, rounded off to two decimal places) is _______.

A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is _______ .

A source transmits a symbol $s$, taken from $\\{-4, 0, 4\\}$ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol $r$ is given by $r = s + w$, where the noise $w$ is zero mean with variance 4 and is independent of $s$.

Using $Q(x) = \frac{1}{\sqrt{2\pi}} \int\limits_{x}^{\infty} e^{-\frac{t^{2}}{2}} dt$, the optimum symbol error probability is _______.